Problem A$.7$

Consider the ODE $y^{\text{'}}P(x)y=f(x).$ If $P(x)$ and $f(x)$ are both constants, then the ODE can be solved by separation of variables. Suppose $P(x)=$a and $f(x)=b,$ where a and $b$ are non$-$zero constants. We then have the ODE $y^{\text{'}}ay=b.$ If $y(0)=c_0,$ solve the initial$-$value problem. Verify by substitution that the explicit solution satisfies the ODE.