Final Answer
$y=e^{-2x^2}\left(\frac{1}{4}e^{2x^2}+C_0\right)$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
1
Simplifying
$\frac{dy}{dx}=x-4xy$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=x-4xy$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x+1*-4xy. Simplifying. Rearrange the differential 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)=4x and Q(x)=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.
Final Answer
$y=e^{-2x^2}\left(\frac{1}{4}e^{2x^2}+C_0\right)$