Exercise
$\frac{\left(1+e^y\right)^2}{e^y}dx+\frac{\left(1+e^x\right)^3}{e^x}dy=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation ((1+e^y)^2)/(e^y)dx+((1+e^x)^3)/(e^x)dy=0. Group the terms of the equation. Multiplying the fraction by -1. 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{e^y}{-1-2e^y-e^{2y}}dy.
Solve the differential equation ((1+e^y)^2)/(e^y)dx+((1+e^x)^3)/(e^x)dy=0
Final answer to the exercise
$\frac{1}{e^y+1}=\frac{1}{-2\left(1+e^x\right)^{2}}+C_0$