Exercise
$\frac{dy}{dx}=e^ycos^2x$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=e^ycos(x)^2. 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 \cos\left(x\right)^2dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(1-\sin\left(x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Solve the differential equation dy/dx=e^ycos(x)^2
Final answer to the exercise
$y=\ln\left(\frac{-1}{\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)+C_0}\right)$