Exercise
$\frac{dy}{dx}=\frac{2}{x}\left(y\right)+x^2e^x$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=2/xy+x^2e^x. Multiplying the fraction by y. Rearrange the differential equation. 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)=x^2e^x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation dy/dx=2/xy+x^2e^x
Final answer to the exercise
$y=\left(e^x+C_0\right)x^{2}$