Question

Solve the differential equation of the following linear differential equation. Show complete solution.

x dy/dx + y = x^3

Answer 1

$x\dfrac{dy}{dx}+y=x^3\\ \dfrac{dy}{dx}+\dfrac{y}{x}=x^2\\ \text{Integrating factor}=e^{\int{\dfrac{1}{x}dx}}=x\\ y\cdot{x}=\int{x\cdot{x^2dx}}+k\\ y\cdot{x}=\dfrac{x^4}{4}+k\\ y=\dfrac{x^3}{4}+\dfrac{k}{x}$