Final answer to the problem
$y=x\left(\cos\left(x\right)+C_0\right)$
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Step-by-step Solution
Learn how to solve factorization problems step by step online. Solve the differential equation dy/dx+xsin(x)=y/x. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x\sin\left(x\right) from both sides of the equation. 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)=\frac{-1}{x} and Q(x)=-x\sin\left(x\right). In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$y=x\left(\cos\left(x\right)+C_0\right)$
