Final answer to the problem
$y=e^{-3x}\left(\frac{e^{3x}x}{3}+\frac{-e^{3x}}{9}+C_0\right)$
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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
Divide both sides of the equation by $dx$
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$\frac{dy}{dx}=\left(x-3y\right)\frac{dx}{dx}$
Learn how to solve problems step by step online. Solve the differential equation dy=(x-3y)dx. Divide both sides of the equation by dx. Simplify the fraction \frac{dx}{dx} by dx. Any expression multiplied by 1 is equal to itself. Rearrange the differential equation.
Final answer to the problem
$y=e^{-3x}\left(\frac{e^{3x}x}{3}+\frac{-e^{3x}}{9}+C_0\right)$
