1
2 2
2
'
y x
xy y
−
=
> 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")
PTVP
Truc x
2
x y
Trang 2> 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")
PTVP
Truc x
3
2 2
> 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)
Trang 3> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main = "PTVP")
PTVP
Truc x
4
x x x
y
y'− sin =sin cos
> 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")
Trang 4166 168 170 172 174 176
PTVP
Truc x
5
x x x
xy
−
1
> 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:
Trang 51: 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
6
) (
2
> 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
Trang 6In 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
2 2 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")
Trang 7166 168 170 172 174 176
PTVP
Truc x
8
x y
x
y ' 1 − 2 + = arcsin
,
0
0 =
=
∞
y
> 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:
Trang 81: 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
Trang 926: 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
9
, ln ln
x x
y
y− =
2
0 2
1
e
y∞= =
> 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")
Trang 10166 168 170 172 174 176
PTVP
Truc x