Final answer to the problem
$y=\sqrt{\frac{2\left(e^x\cdot x-e^x+C_0\right)}{3}},\:y=-\sqrt{\frac{2\left(e^x\cdot x-e^x+C_0\right)}{3}}$
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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
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1
Divide both sides of the equation by $dx$
$\frac{3\ln\left(y\cdot dy\right)}{dx}=xe^x\frac{dx}{dx}$
Learn how to solve problems step by step online.
$\frac{3\ln\left(y\cdot dy\right)}{dx}=xe^x\frac{dx}{dx}$
Learn how to solve problems step by step online. Solve the differential equation 3ln(ydy)=xe^xdx. 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. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality.
Final answer to the problem
$y=\sqrt{\frac{2\left(e^x\cdot x-e^x+C_0\right)}{3}},\:y=-\sqrt{\frac{2\left(e^x\cdot x-e^x+C_0\right)}{3}}$
