Final Answer
Step-by-step Solution
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Factor the polynomial $xe^{-y}+10e^{-y}$ by it's greatest common factor (GCF): $e^{-y}$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=e^{-y}\left(x+10\right)$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=xe^(-y)+10e^(-y). Factor the polynomial xe^{-y}+10e^{-y} by it's greatest common factor (GCF): e^{-y}. 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. Integrate both sides of the differential equation, the left side with respect to . Expand the integral \int\left(x+10\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.