Exercise
$xy'+2y=e^x\:\:\:y\left(1\right)=1$
Step-by-step Solution
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation xy^'+2y=e^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)=\frac{e^x}{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=e^x
Final answer to the exercise
$y=\frac{e^x\cdot x-e^x+1}{x^2}$