Learn how to solve problems step by step online. Solve the differential equation (-dy)/dx+y=-x^2-2x+9. Eliminate the minus (-) sign from the differential by multiplying the whole differential equation by -1. 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)=-1 and Q(x)=-\left(-x^2-2x+9\right). 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. So the integrating factor \mu(x) is.

Solve the differential equation (-dy)/dx+y=-x^2-2x+9