Problem $1$: Solve the following ordinary differential equations that are important in heat transfer:

$\frac{dy}{dx}+y=0$

$\frac{dy}{dx}+y+=0$

$\frac{d^{2}y}{d{x}^2}-{}^{2}y=0$

$\frac{d^{2}y}{d{x}^2}+{}^{2}y=0$

$\frac{d^{2}y}{d{x}^2}+{}^{2}y+=0$

where $,,$ and $$ are constants.