Step-by-step Solution

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Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=xe^{-y}$

Learn how to solve differential equations problems step by step online.

$\frac{1}{e^{-y}}dy=x\cdot dx$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=xe^(-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. Integrate both sides, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{e^{-y}}dy and replace the result in the differential equation. Solve the integral \int xdx and replace the result in the differential equation.

$y=\ln\left(\frac{1}{2}x^2+C_0\right)$

Problem Analysis

$\frac{dy}{dx}=xe^{-y}$

Main topic:

Differential equations

~ 0.05 seconds