Find the general solution to each differential equation below $($all integrating constants should be written as $\text{'}$ C $\text{'}).$ What is the solution satisfying $y(3)=2?$

a$)\frac{dy}{dx}=x^3+2x$

General Solution: $y=$

Solution satisfying $y(3)=2$ : $y=$

b$)\frac{dy}{dx}=3cosx$

General Solution: $y=$

Solution satisfying $y(3)=2$:$y=$

c$)\frac{dy}{dx}=\frac{5}{x},$ where $x>0$

General Solution: $y=$

Solution satisfying $y(3)=2$ : $y=$