Exercise
$ty'+2ty=3t$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation ty^'+2ty=3t. Rewrite the differential equation using Leibniz notation. Divide all the terms of the differential equation by t. 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(t)=2 and Q(t)=3. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation ty^'+2ty=3t
Final answer to the exercise
$y=e^{-2t}\left(\frac{3e^{2t}}{2}+C_0\right)$