How to solve differential equation

2 次查看（过去 30 天）

显示更早的评论

Swati Sarangi 2020-1-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/502523-how-to-solve-differential-equation

评论： Bjorn Gustavsson 2020-1-29

Hi ,

Can someone check my codes written below and find out the error in it?

1.dx/dt +x^2=0 , x(0)=x0 --> The solution should be x(t)=x0*exp((-x^2 )*t)

syms x(t) a x0

Dx=diff(x)

dsolve(Dx==-x.^2,x(0)==x0)

I'm getting

ans =1/(t + 1/x0) which I know, is wrong.

2.d2y/dt2+ w^2y=0 y(0)=y0 , dy/dt(0)=v0

My code:

syms y(t) w y0 v0

Dy=diff(y)

D2y=diff(y,2)

dsolve(D2y==-w^y, y(0)==y0,Dy(0)==v0)

Regards

Swati

4 个评论
显示 2更早的评论隐藏 2更早的评论

Walter Roberson 2020-1-29

If hypothetically there were an exponential term in the solution then it would have to be exponential in t and not x.

Have you taken your proposed exponential solution and substituted it into the differential equation to verify that it works? I believe that you will find that it does not work.

Bjorn Gustavsson 2020-1-29

That nonlinear differential equation can be solved with separation of variables.

You get:

That one you integrate from t0 to t giving you the solution matlab gave you. For a general solution of ODEs of this kind have a look at: Ricatti equation.

请先登录，再进行评论。

请先登录，再回答此问题。