Exercise
$\frac{dy}{dx}=\frac{e^{-y}+e^{-5x-y}}{\left(ye^x\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(e^(-y)+e^(-5x-y))/(ye^x). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Factoring by 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. Simplify the expression \frac{y}{e^{-y}}dy.
Solve the differential equation dy/dx=(e^(-y)+e^(-5x-y))/(ye^x)
Final answer to the exercise
$e^y\cdot y-e^y=\frac{1}{-6e^{6x}}+\frac{1}{-e^x}+C_0$