Your integration of the ode is fine, but you've gone astray with the very last line.
It makes life easier if, in this case, you let the constant of integration be That allows you to get rid of the negative signs.
Now if you take the reciprocal both sides (and that's the whole of the RHS including the and shunt the to the other side of the equation, you have
Your second example is of the integrating factor type. Start by dividing throughout by and then multiply throughout by the integrating factor
where is the coefficient of in the second term (after the division by and including the negative sign).
I fear that you will struggle with the integral of the resulting RHS though. Check that you've copied the question correctly.