Exercise
$\frac{dy}{dx}=2x.e^{-y}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=2xe^(-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. Simplify the expression \frac{1}{e^{-y}}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int e^ydy and replace the result in the differential equation.
Solve the differential equation dy/dx=2xe^(-y)
Final answer to the exercise
$y=\ln\left(x^2+C_0\right)$