Exercise
$y'\:=xy+9x$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=xy+9x. Rewrite the differential equation using Leibniz notation. Rearrange the differential equation. 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)=-x and Q(x)=9x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Solve the differential equation y^'=xy+9x
Final answer to the exercise
$y=-9+C_0e^{\frac{1}{2}x^2}$