Solving a Linear First-Order ODE
Consider the differential equation \(\frac{dy}{dx} = \frac{y}{x} + x\) for \(x > 0\). (a) Briefly justify why the equation is not directly separable, but is a linear first-order ODE. (b) Solve the differential equation and express the general solution in the form \(y = x^2 + Cx\), where \(C\) is an arbitrary constant.