Thread: Is this sine equation solvable

Hi,

I need to either solve or prove that the resolution of the following ODE is impossible;



Mathemtatica refuse solving it rather giving

" InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses."

Any help would be highly apreciated, thank you

Isatis55

Hey isatis55.

I haven't taken DE's for a while but the output suggests that f(x) is not a unique function (with the multi-valued comment) and this implies that y(x) doesn't exist since it has to be unique by definition to give a function (functions must be unique and give one output for every input).

Originally Posted by isatis55

Hi,

I need to either solve or prove that the resolution of the following ODE is impossible;



Mathemtatica refuse solving it rather giving

" InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses."

Any help would be highly apreciated, thank you

Isatis55

If you multiply the equation by

This gives



Now the differential equation can be put in its self-adjoint form



This is a Sturm-Liouville differential equation.

The boundary or initial conditions determine if the equation has solutions.

For example if you require

The equation will have only the trivial solution

Great, thanks a lot.

I am now altering the initial problem and I am again faced against a non linear differential equation given by

[math] y''(x)+a*y'(x)^2+b*y'(x)+c*y(x) + c*sin(d*t) + e = 0 [\math]

Do you think it is solvable?

PS: I definitely need a course on ODE.