Exact differential equations. Test to tel if its exact not valid, am I doing something wrong? I got this differential equation:
$$(y^{3} + \cos t)'y = 2 + y \sin t,\text{ where }y(0) = -1$$
Tried to check for $dM/dY = dH/dY$ but I cant seem to get them alike. So what would the next step be to solve this problem?

If it is really
$$\left(y(t)^{3}+\cos(t)\right)y'(t)=2+y(t)\sin(t)$$ I do not see, why the ode should not be exact.
Let $M(y,t):=-2-y\sin(t)$ and $H(y,t):=y^3+\cos(t)$, the condition for exactness
$$\frac{dM(y,t)}{dy}=\frac{dH(y,t)}{dt}$$ does not fail...
