Solving the Differential Equation

[Manni]

I'm given the differential dy/dx = x*y*sinx / (y+1) and I need to find its solution.

I apply the following steps,

(y+1)/y*dy = x*sinx*dx

1 + 1/y*dy = x*sinx*dx

∫ 1 + 1/y*dy = ∫ x*sinx*dx

...skipping a few steps for convenience I get the equation

y + lny = -x*cosx + sinx

My problem now is that I don't know how do I solve for y.

 

[Dick]

I'm given the differential dy/dx = x*y*sinx / (y+1) and I need to find its solution.

I apply the following steps,

(y+1)/y*dy = x*sinx*dx

1 + 1/y*dy = x*sinx*dx

∫ 1 + 1/y*dy = ∫ x*sinx*dx

...skipping a few steps for convenience I get the equation

y + lny = -x*cosx + sinx

My problem now is that I don't know how do I solve for y.

You can't solve nicely for y. That's often the case. But you've gotten rid of the derivatives, that should be enough. I do miss seeing an arbitrary constant (a '+C') somewhere in your solution.