非线性微分方程

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SDFG ASDF
SDFG ASDF on 9 Apr 2022
Commented: SDFG ASDF on 26 Apr 2022
我想问一下下面这个非线性微分方程有没有精确解,以及我根据Matlab的帮助文档,只得到了一组隐式解,有没有办法得到一组精确解?
syms y(x) a
eqn = diff(y,x,2)==-a.*(1-(y.^2)./2)
Dy = diff(y,x)
cond = [y(0)==0,Dy(1)==0]
s = dsolve(eqn,cond,'Implicit',true)
运行后的结果
a*y(x)^3 - 6*a*y(x) == 0

Answers (1)

埃博拉酱
埃博拉酱 on 24 Apr 2022
Edited: 埃博拉酱 on 24 Apr 2022
>> s = dsolve(eqn,cond)
警告: Unable to find symbolic solution.
没有精确解。
这没什么奇怪的,一个一般的微分方程大概率没有精确解。
  1 Comment
SDFG ASDF
SDFG ASDF on 26 Apr 2022
谢谢!我在Mathematic上尝试求解得到的是一个含有未知常数的椭圆函数解,所以我想继续尝试求解得到精确解,但求不出来。

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