Exercise
$\left(e^y+1\right)^2e^{-y}dx\:=\:-\left(e^x+1\right)^3dy$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (e^y+1)^2e^(-y)dx=-(e^x+1)^3dy. 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}{\left(e^y+1\right)^2e^{-y}}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Since the exponent of the denominator is negative, we can bring it to the numerator and thus simplify.
Solve the differential equation (e^y+1)^2e^(-y)dx=-(e^x+1)^3dy
Final answer to the exercise
$\frac{1}{-\left(e^y+1\right)}=\frac{-1}{2\left(e^x+1\right)^{2}}-x+\ln\left|e^x+1\right|+\frac{-1}{e^x+1}+C_0$