Exercise
$y'=e^x+y-e^{-x}y^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=e^x+y-e^(-x)y^2. Rewrite the differential equation using Leibniz notation. 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)=-1 and Q(x)=e^x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation y^'=e^x+y-e^(-x)y^2
Final answer to the exercise
$y=\left(x+C_0\right)e^x$