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- Exact Differential Equation
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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 $P(x)=-2x$ and $Q(x)=x$. In order to solve the differential equation, the first step is to find the integrating factor $\mu(x)$
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$\displaystyle\mu\left(x\right)=e^{\int P(x)dx}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx-2xy=x. 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)=-2x and Q(x)=x. 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. Now, multiply all the terms in the differential equation by the integrating factor \mu(x) and check if we can simplify.
