Answer to Question #244280 in Electrical Engineering for Jac

Question #244280

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


x dy/dx + y = x^3


1
Expert's answer
2021-10-01T16:47:02-0400

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


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