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Divide all the terms of the differential equation by $\left(x+2\right)^2$
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$\frac{\left(x+2\right)^2}{\left(x+2\right)^2}\frac{dy}{dx}+\frac{\left(8+4x\right)y}{\left(x+2\right)^2}=\frac{5}{\left(x+2\right)^2}$
Learn how to solve problems step by step online. Solve the differential equation (x+2)^2dy/dx+(8+4x)y=5. Divide all the terms of the differential equation by \left(x+2\right)^2. 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{8+4x}{\left(x+2\right)^2} and Q(x)=\frac{5}{\left(x+2\right)^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.