First Order Differential Equation Verification

I've tried the differential equations below plenty of times but my answers and the answer given in the textbook do not match. Can anyone please verify the answers for me? Thank you so much!

1) $\frac{\mathrm{d} v}{\mathrm{d} t} + ay = e^{bt}$

2) $\sin(x)\frac{\mathrm{d} y}{\mathrm{d} x} + 2y\cos(x) = \cos(x)$

My answers (here, c is some arbitrary constant):

1) $v = \dfrac{1}{a + b}(e^{bt} - e^{-at})$

2) $y\sin^2(x) = -\dfrac{1}{4} \cos(2x) + c$

Did you write eqn.(1) correctly?

Solution 2 looks good. Rearrange it for $y$ since you can.

Thank you so much! There was a small error in eqn(1). I have fixed it now.

Solution to eqn, 1 is good too if you include the arbitrary constant in the correct place.