Solve ODE without initial condition

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 ]

Answer 1

[Torsten]

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.

[sudhir]

THANK YOU

Answer 2

[Sam Chak]

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.

[Torsten]

Impressive that Wolfram Alpha was able to deduce this.

Maybe better: "implicit" instead of "recurrence" for the solution given.

[Sam Chak]

Yes, implicit solution.