Chapter 8.1, Problem 1QCE

Match each differential equation with its family of solutions.

$\begin{array}{l}\text{(a)}x\frac{dy}{dx}=y\text{\_\_\_\_\_}(\text{i)}y=x^2+C\\ \text{(b) }y"=4y\text{\_\_\_\_\_}(\text{ii)}y=C_1\sin 2x+C_2\cos 2x\\ \text{(c) }\frac{dy}{dx}=2x\text{\_\_\_\_\_}\text{(iii)}y=C_1{e}^{2x}+C_2{e}^{-2x}\\ \text{(d)}\frac{d^{2}y}{d{x}^2}=-4y\text{\_\_\_\_\_}\text{(iv)}y=Cx\end{array}$