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Solve ODE without initial condition

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sudhir
sudhir 2023-11-20
评论： Sam Chak 2023-11-20
syms y(x) x
E=diff(y,x)+(y*cos(x)+sin(y)+y)/(sin(x)+x*cos(y)+x)==0
y=(dsolve(E))
I am getting error
E(x) =
Warning: Unable to find symbolic solution.
y =[ empty sym ]

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回答（2 个）

Torsten
Torsten 2023-11-20
Your ODE is nonlinear. The symbolic toolbox is not able to find an analytical solution for it. You will only be able to solve it numerically with a given initial condition.
Sam Chak
Sam Chak 2023-11-20
Hi @sudhir
I also couldn't obtain the analytical solution using dsolve(). However, when I tested this problem on Wolfram Alpha, it returned an open-form solution that manifests in the form of a recurrence relation.
  2 个评论
Torsten
Torsten 2023-11-20
Impressive that Wolfram Alpha was able to deduce this.
Maybe better: "implicit" instead of "recurrence" for the solution given.

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