Part 2

1. Find the gerneral solution of $\frac{dy}{dx}+\sin x +y \cos x= \cos x+ y\sin x$.

2. Find the general solution of $\frac{dy}{dx}+ \frac{1}{x} y = 1$.

3. Find the solution to $y^{\prime \prime}-8y^{\prime}+17y=0$ that satisfy the conditions $y(0)=1$, $y^{\prime}(0)=-1$.

4. Suppose it takes 6 days for 25% of a radioactive substance to decay.
   1. What is the half-life of the substance?
   2. How long does it take for 75% of the substance to decay?