Final answer to the problem
$y=e^{-2x}\left(5e^{2x}+C_0\right)$
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Step-by-step Solution
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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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1
Rewrite the differential equation using Leibniz notation
$x\frac{dy}{dx}+2xy=10x$
Learn how to solve differential equations problems step by step online.
$x\frac{dy}{dx}+2xy=10x$
Learn how to solve differential equations problems step by step online. Solve the differential equation xy^'+2xy=10x. Rewrite the differential equation using Leibniz notation. 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)=2 and Q(x)=10. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Final answer to the problem
$y=e^{-2x}\left(5e^{2x}+C_0\right)$
