91Ó°ÊÓ

Solve the differential equations in Exercises \(1-14\) $$ (1+x) y^{\prime}+y=\sqrt{x} $$

In Exercises \(7-10\) , write an equivalent first-order differential equation and initial condition for \(y .\) $$ y=-1+\int_{1}^{x}(t-y(t)) d t $$

Solve the exponential growth/decay initial value problem for \(y\) as a function of \(t\) by thinking of the differential equation as a first-order linear equation with \(P(x)=-k\) and \(Q(x)=0 :\) $$\frac{d y}{d t}=k y \quad(k\( constant \)), \quad y(0)=y_{0}$$