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