Exercise
$y'-\frac{2}{t}y=t,\:y\left(1\right)=2$
Step-by-step Solution
Learn how to solve classify algebraic expressions problems step by step online. Solve the differential equation y^'+-2/ty=t. Multiplying the fraction by y. Rewrite the differential equation using Leibniz notation. 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)=\frac{-2}{t} and Q(t)=t. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(t), we first need to calculate \int P(t)dt.
Solve the differential equation y^'+-2/ty=t
Final answer to the exercise
$y=\left(\ln\left(t\right)+2\right)t^{2}$