Exercise
$2xy'-y=x^3-x$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation 2xy^'-y=x^3-x. Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by 2x. 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}{2x} and Q(x)=\frac{x^3-x}{2x}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation 2xy^'-y=x^3-x
Final answer to the exercise
$y=\left(\frac{\sqrt{x^{5}}}{5}-\sqrt{x}+C_0\right)\sqrt{x}$