Exercise
$y'\:+\:2xy\:+\:x\:=\:e^{-x^2}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'+2xyx=e^(-x^2). Rewrite the differential equation using Leibniz notation. Group the terms of the equation. 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)=2x and Q(x)=e^{-x^2}-x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Solve the differential equation y^'+2xyx=e^(-x^2)
Final answer to the exercise
$y=e^{-x^2}\left(x+\frac{-e^{\left(x^2\right)}}{2}+C_0\right)$