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Solve ODE without initial condition

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sudhir
sudhir on 20 Nov 2023
Commented: Sam Chak on 20 Nov 2023
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 ]

Answers (2)

Torsten
Torsten on 20 Nov 2023
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 on 20 Nov 2023
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 Comments
Torsten
Torsten on 20 Nov 2023
Impressive that Wolfram Alpha was able to deduce this.
Maybe better: "implicit" instead of "recurrence" for the solution given.

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