Bài tập Toán Cao Cấp 2

y' =

2 xy
x − y2
2

1.
> ham <- function (x, y,parms) {list(c((2*x)/(1+x^2)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")

2.00

2.02

2.04

2.06

Truc y

2.08

2.10

2.12

PTVP

166

168

170

172
Truc x

2.

y '+ y = 4 x

174

176


> ham <- function (x, y,parms) {list(c(-y+4*x))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")

0

100

200

300

Truc y

400

500

600

700

PTVP

166

168

170

172

174

Truc x

y '+2 xy = xe − x

2

3.
> ham <- function (x, y,parms) {list(c(-2*x*y+x*exp(-x^2)))}

> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)

176


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

0.0

0.5

1.0

Truc y

1.5

2.0

PTVP

166

168

170

172

174

176

Truc x

4.

y '− y. sin x = sin x cos x

> 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 = 166:176, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")


0.0

0.5

1.0

Truc y

1.5

2.0

PTVP

166

168

170

172

174

Truc x

y '+
5.

xy
= arcsin x + x
1− x2

> 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 = 166:176, parms = 0)
There were 14 warnings (use warnings() to see them)
> warnings()
Warning messages:

176


1: In asin(x) : NaNs produced

2: In asin(x) : NaNs produced
3: In asin(x) : NaNs produced
4: In asin(x) : NaNs produced
5: In asin(x) : NaNs produced
6: In asin(x) : NaNs produced
7: In asin(x) : NaNs produced
8: In asin(x) : NaNs produced
9: In asin(x) : NaNs produced
10: In asin(x) : NaNs produced
11: In asin(x) : NaNs produced
12: In asin(x) : NaNs produced
13: In asin(x) : NaNs produced
14: In asin(x) : NaNs produced

y ' = 2 x( x 2 + y )
6.
> ham <- function (x, y,parms) {list(c(2*x*(x^2+y)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
DINTDY- T (=R1) illegal
In above message, R1 = 169

T not in interval TCUR - HU (= R1) to TCUR (=R2)
In above message, R1 = 168.077, R2 = 168.077

DINTDY- T (=R1) illegal


In above message, R1 = 170

T not in interval TCUR - HU (= R1) to TCUR (=R2)
In above message, R1 = 168.077, R2 = 168.077

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

In above message, R1 = 170

Error in lsoda(y, times, func, parms, ...) :
illegal input detected before taking any integration steps - see written message

7.

xy '−2 y = 2 x 2

> ham <- function (x, y,parms) {list(c((2*y)/x+2*x^3))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")


0e+00

2e+07

4e+07

Truc y

6e+07

8e+07

1e+08

PTVP

166

168

170

172

174

Truc x

y '. 1 − x 2 + y = arcsin x
8.

,

y ∞=0 = 0

> ham <- function (x, y,parms) {list(c(-y/sqrt(1-x^2)+asin(x)/sqrt(1-x^2)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
There were 42 warnings (use warnings() to see them)

> warnings()
Warning messages:

176


1: In sqrt(1 - x^2) : NaNs produced
2: In asin(x) : NaNs produced
3: In sqrt(1 - x^2) : NaNs produced
4: In sqrt(1 - x^2) : NaNs produced
5: In asin(x) : NaNs produced
6: In sqrt(1 - x^2) : NaNs produced
7: In sqrt(1 - x^2) : NaNs produced
8: In asin(x) : NaNs produced
9: In sqrt(1 - x^2) : NaNs produced
10: In sqrt(1 - x^2) : NaNs produced
11: In asin(x) : NaNs produced
12: In sqrt(1 - x^2) : NaNs produced
13: In sqrt(1 - x^2) : NaNs produced
14: In asin(x) : NaNs produced
15: In sqrt(1 - x^2) : NaNs produced
16: In sqrt(1 - x^2) : NaNs produced
17: In asin(x) : NaNs produced
18: In sqrt(1 - x^2) : NaNs produced
19: In sqrt(1 - x^2) : NaNs produced
20: In asin(x) : NaNs produced
21: In sqrt(1 - x^2) : NaNs produced
22: In sqrt(1 - x^2) : NaNs produced
23: In asin(x) : NaNs produced
24: In sqrt(1 - x^2) : NaNs produced

25: In sqrt(1 - x^2) : NaNs produced


26: In asin(x) : NaNs produced
27: In sqrt(1 - x^2) : NaNs produced
28: In sqrt(1 - x^2) : NaNs produced
29: In asin(x) : NaNs produced
30: In sqrt(1 - x^2) : NaNs produced
31: In sqrt(1 - x^2) : NaNs produced
32: In asin(x) : NaNs produced
33: In sqrt(1 - x^2) : NaNs produced
34: In sqrt(1 - x^2) : NaNs produced
35: In asin(x) : NaNs produced
36: In sqrt(1 - x^2) : NaNs produced
37: In sqrt(1 - x^2) : NaNs produced
38: In asin(x) : NaNs produced
39: In sqrt(1 - x^2) : NaNs produced
40: In sqrt(1 - x^2) : NaNs produced
41: In asin(x) : NaNs produced
42: In sqrt(1 - x^2) : NaNs produced

y '−

9.

y
= x ln x,
x ln x

y ∞ =0 =

1 2
e
2

> ham <- function (x, y,parms) {list(c(y/log(x)+x*log(x)))}
> dieukien <- c(y = 2)
> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)
> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")


0

5000

10000

15000

Truc y
20000

25000

PTVP

166
168
170
172

Truc x
174
176