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Divide all the terms of the differential equation by $x+1$
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$\frac{x+1}{x+1}\frac{dy}{dx}+\frac{y}{x+1}=\frac{x^2-1}{x+1}$
Learn how to solve simplification of algebraic expressions problems step by step online. Solve the differential equation dy/dx(x+1)+y=x^2-1. Divide all the terms of the differential equation by x+1. 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)=\frac{1}{x+1} and Q(x)=x-1. 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.