sử dụng phần mềm R

Nhiệm vụ 3:Bài 10.4
1) y’=
>library(deSolve)
> ham <- function (x, y,parms) {list(c((2*x)/(1+x^2)*y))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")


2) y’+ y = 4x
> library(deSolve)
> ham <- function (x, y,parms) {list(c(-y+4*x))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times =164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")


3) y’ + 2xy = x

> library(deSolve)
> ham <- function (x, y,parms) {list(c(-2*x*y + x*exp(-1)^(x^2)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times =164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")
>


4) y’ – ysinx = sinxcosx

> library(deSolve)
> ham <- function (x, y,parms) {list(c(y*sin(x)+ sin(x)*cos(x)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times =164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")

>


5) y’+ = arcsinx +x
> library(deSolve)
> ham <- function (x, y,parms) {list(c(-x*y/(1-x^2)+ asin(x)+ x))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
There were 14 warnings (use warnings() to see them)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")
>


6) y’ = 2x (+y)
> library(deSolve)
> ham <- function (x, y,parms) {list(c(2*x*(x^2+y)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
DINTDY- T (=R1) illegal
In above message, R1 = 167

T not in interval TCUR - HU (= R1) to TCUR (=R2)

In above message, R1 = 166.102, R2 = 166.102

DINTDY- T (=R1) illegal
In above message, R1 = 168

T not in interval TCUR - HU (= R1) to TCUR (=R2)
In above message, R1 = 166.102, R2 = 166.102

DLSODA- Trouble in DINTDY. ITASK = I1, TOUT = R1
In above message, I1 = 1

In above message, R1 = 168

Error in lsoda(y, times, func, parms, ...) :
illegal input detected before taking any integration steps - see written message
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")


>


7) xy’ – 2y = 2
> library(deSolve)
> ham <- function (x, y,parms) {list(c((2*y+2*x^4)/x))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")

8) y’ + y = arcsin x
> library(deSolve)
> ham <- function (x, y,parms) {list(c((-y + asin(x))/ sqrt(1-x^2)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
There were 28 warnings (use warnings() to see them)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")
>


9) y’ - = x lnx
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y/(x*log(x))+ x*log(x)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =
"PTVP")
>


Nhiệm vụ 4:Bài 10.7
1) y” – 2y’ – y = 0
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 2 * y[2] + y[1]))}
> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")

1.0e+10
5.0e+09
0.0e+00

Truc y

1.5e+10

2.0e+10

PTVP cấp 2

164

166

168

170
time

172

174


2) y” – 9y = cosx
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 9 * y[1] + exp(3)^x cos(x)))}
Error: unexpected symbol in "ham <- function (x, y,parms) {list(c(y[2], 9 * y[1] +

exp(3)^x cos"
> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-119

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-119

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-115

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.


In above message, R1 = 164, R2 = 2.59823e-115

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-115

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-114

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-114

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-114

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-114


DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 2.59823e-113

DLSODA- Above warning has been issued I1 times.
It will not be issued again for this problem.
In above message, I1 = 10

> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>


3) 4y” – 20y’ + 25y = 0
> library(deSolve)
> ham <- function (x, y,parms) {list(c(4*y[2], 20 * y[2] - 25* y[1]))}
> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>


4) y” – 4y’= -12 – 6x - 4
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 4 * y[2] - 12*x - 6*x - 4 ))}
> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>


5) y” – 2y’ – 3y =
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 2 * y[2] + 3 * y[1] + exp(4)^x))}
> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step

(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 0

DINTDY- T (=R1) illegal
In above message, R1 = 165

T not in interval TCUR - HU (= R1) to TCUR (=R2)
In above message, R1 = 164, R2 = 164

DINTDY- T (=R1) illegal
In above message, R1 = 166

T not in interval TCUR - HU (= R1) to TCUR (=R2)
In above message, R1 = 164, R2 = 164

DLSODA- Trouble in DINTDY. ITASK = I1, TOUT = R1
In above message, I1 = 1

In above message, R1 = 166

Error in lsoda(y, times, func, parms, ...) :
illegal input detected before taking any integration steps - see written message
> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>


6) y” – 5y’ + 4y = 4
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 5 * y[2] - 4 * y[1] + 4 * x^2 * exp(1)^x))}

> dieukien <- c(y1 = 2, y2 = 1)


> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-79

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-79

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-75

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-75

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-75

DLSODA- Warning..Internal T (=R1) and H (=R2) are

such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-74

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-74

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-74

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-74

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.10914e-73

DLSODA- Above warning has been issued I1 times.
It will not be issued again for this problem.
In above message, I1 = 10

> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>

7) y” – y = 2 sin x – 4 cos x
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], y[1] + 2 * sin(x) - 4 * cos(x)))}
> dieukien <- c(y1 = 2, y2 = 1)


> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")
>

8) y” – 4y =
> library(deSolve)
> ham <- function (x, y,parms) {list(c(y[2], 4*y[1] + exp(1)^x*((-4*x +4)*cos(x)- (2*x +
6)*sin(x))))}


> dieukien <- c(y1 = 2, y2 = 1)
> nghiem <- ode(y = dieukien, func = ham,times = 164:174, parms = 1)
DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-77

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.

In above message, R1 = 164, R2 = 1.65096e-77

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-73

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-73

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-73


DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-72

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-72

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step

(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-72

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-72

DLSODA- Warning..Internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). Solver will continue anyway.
In above message, R1 = 164, R2 = 1.65096e-71

DLSODA- Above warning has been issued I1 times.
It will not be issued again for this problem.