Analytic solution for an ODE - 未名空间MITBBS历史存档

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Analytic solution for an ODE

Analytic solution for an ODE# Computation - 科学计算

w*g2002-05-23 07:05

1 楼

I need to find the analytic solution for the following ODE:
y''(x)=a*exp(4y)+b
Any big shrimp can help me?

b*y2002-05-23 07:05

2 楼

try matlab symbolic toolbox:
y=dsolve('D2y=a*exp(4*y)+b');

【在 w*******g 的大作中提到】

: I need to find the analytic solution for the following ODE:
: y''(x)=a*exp(4y)+b
: Any big shrimp can help me?

w*g2002-05-23 07:05

3 楼

Could you please tell me the results? I could not access Matlab right now...
Thank you very much!

【在 b*****y 的大作中提到】

: try matlab symbolic toolbox:
: y=dsolve('D2y=a*exp(4*y)+b');

l*i2002-05-23 07:05

4 楼

-2*Int(1/(2*a*exp(4*a)+8*b*a+4*C1)^(1/2),a=``..y)-t-C2=0
2*Int(1/(2*a*exp(4*a)+8*b*a+4*C1)^(1/2),a=``..y)-t-C2=0

【在 w*******g 的大作中提到】

: Could you please tell me the results? I could not access Matlab right now...
: Thank you very much!

b*y2002-05-23 07:05

5 楼

The following is the full turn-out in matlab 6.0:
>> y=dsolve('D2y=a*exp(4*y)+b')
Warning: Explicit solution could not be found; implicit solution returned.
> In /usr/local/matlab6/toolbox/symbolic/dsolve.m at line 292
y =
[ 2*Int(1/(2*a*exp(4*a)+8*b*a+4*C1)^(1/2),a=``..y)-t-C2=0,
-2*Int(1/(2*a*exp(4*a)+8*b*a+4*C1)^(1/2),a=``..y)-t-C2=0]
>> pretty(y)
[ y
[ /
[ | 1
[2 | -------------------------------- da - t - C2 = 0 ,
[ |

【在 w*******g 的大作中提到】

: Could you please tell me the results? I could not access Matlab right now...
: Thank you very much!

w*g2002-05-23 07:05

6 楼

I don't think Matlab can do a good job on this. I tried the following ODE:
d dy

b*y2002-05-23 07:05

7 楼

I guess Matlab uses the symbolic computing engine of Maple. I won't
cast much doubt on the correctness of the solution but rather check
on its final form of representation which is most likely confusing.

【在 w*******g 的大作中提到】

: I don't think Matlab can do a good job on this. I tried the following ODE:
: d dy