Answer to Question #244281 in Differential Equations for Jac

Question

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

x dy/dx + y = x^3

Answer 1

Let us solve the differential equation $x y'+ y = x^3,$ which is equivalent to the equation $(x y)' = x^3.$ It follows that $xy=\frac{x^4}4+C.$ Therefore, the general solution is of the form:

$y=\frac{x^3}4+\frac{C}x.$