Final answer to the problem
$\frac{1}{2}y^2=\frac{1}{-3e^{3\left(x+2-2\right)}}+\frac{-\frac{1}{e^{4}}}{e^x}+C_0$
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Step-by-step Solution
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- Exact Differential Equation
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1
Calculate the power $e^{-4}$
$\frac{ye^xdy}{dx}=\frac{1}{e^{4}}+e^{\left(-2x-4\right)}$
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$\frac{ye^xdy}{dx}=\frac{1}{e^{4}}+e^{\left(-2x-4\right)}$
Learn how to solve problems step by step online. Solve the differential equation (ye^xdy)/dx=e^(-4)+e^(-2x-4). Calculate the power e^{-4}. 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. Simplify the expression \frac{\frac{1}{e^{4}}+e^{\left(-2x-4\right)}}{e^x}dx. Integrate both sides of the differential equation, the left side with respect to .
Final answer to the problem
$\frac{1}{2}y^2=\frac{1}{-3e^{3\left(x+2-2\right)}}+\frac{-\frac{1}{e^{4}}}{e^x}+C_0$