Exercise
$\frac{dy}{dx}=\frac{8e^{4x-y}}{y}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(8e^(4x-y))/y. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation dy/dx=(8e^(4x-y))/y
Final answer to the exercise
$e^y\cdot y-e^y=2e^{4x}+C_0$