Exercise
$x\cdot y'-y=2\cdot\left(x^3\right)\cdot lnx$
Step-by-step Solution
Learn how to solve special products problems step by step online. Solve the differential equation xy^'-y=2x^3ln(x). Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by x. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{-1}{x} and Q(x)=2x^{2}\ln\left(x\right). In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation xy^'-y=2x^3ln(x)
Final answer to the exercise
$y=\left(x^2\ln\left(x\right)+\frac{-x^2}{2}+C_0\right)x$