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- Exact Differential Equation
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Rearrange the differential equation
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$\frac{dy}{dx}-\left(y+5e^{\frac{x}{2}}\cos\left(5x\right)\right)=-\frac{1}{2}e^{\frac{x}{2}}\sin\left(5x\right)$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=-1/2e^(x/2)sin(5x)+5e^(x/2)cos(5x)y. 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)=-1 and Q(x)=-\frac{1}{2}e^{\frac{x}{2}}\sin\left(5x\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.
