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Divide all the terms of the differential equation by $t^2+1$
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$\frac{t^2+1}{t^2+1}\frac{dw}{dt}+\frac{tw}{t^2+1}=\frac{t}{t^2+1}$
Learn how to solve differential equations problems step by step online. Solve the differential equation (t^2+1)dw/dt+tw=t. Divide all the terms of the differential equation by t^2+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(t)=\frac{t}{t^2+1} and Q(t)=\frac{t}{t^2+1}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(t), we first need to calculate \int P(t)dt.