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** Step-by-step Solution **

** How should I solve this problem?

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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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Divide all the terms of the differential equation by $x$

Learn how to solve differential equations problems step by step online.

$\frac{x}{x}\frac{dy}{dx}+\frac{-2y}{x}=\frac{x^3\cos\left(x\right)}{x}$

Learn how to solve differential equations problems step by step online. Solve the differential equation xdy/dx-2y=x^3cos(x). Divide all the terms of the differential equation by x. 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{-2}{x} and Q(x)=x^{2}\cos\left(x\right). 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.

** Final answer to the problem

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