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Rearrange the differential equation
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$\frac{dy}{dx}-\left(-20y+2x\right)=20x^2$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=-20y+20x^22x. Rearrange the differential equation. 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)=20 and Q(x)=20x^2. 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.