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