Final answer to the problem
Step-by-step Solution
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Divide all terms of the equation by $x-1$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}+\frac{y}{x-1}=\frac{\ln\left(x\right)}{x-1}$
Learn how to solve differential equations problems step by step online. Solve the differential equation ((x-1)dy)/dx+y=ln(x). Divide all terms of the equation by x-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)=\frac{1}{x-1} and Q(x)=\frac{\ln\left(x\right)}{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. So the integrating factor \mu(x) is.