Is this equation solvable and if so, how?

[MecEngStudent]

xy'=3y+(cosx)x^4

I don't understand how to solve it since it's non-separable.

 

[ap_nhp]

y'/x^3-3y/x^4=cosx

d/dx(y/x^3)=cosx

y/x^3=sinx

y=(sinx)x^3

 

[l'Hôpital]

I don't understand how to solve it since it's non-separable.

There's more to Differential Equations than just the separable ones. A LOT more.

 

[kosovtsov]

Surely

d/dx(y/x^3)=cosx

y/x^3=sinx+C

y=(sinx+C)x^3

where C is an arbitrary constant.

 

[blue_raver22]

The equation xy'=3y+(cosx)x^4 is indeed non-separable, meaning it cannot be solved using traditional methods such as separation of variables. However, it is still possible to find a solution using numerical methods or by approximating the solution using a series expansion. Alternatively, one could also use software or programming to solve the equation numerically.