Exercise
$\frac{dy}{dt}=cos\left(t\right)\left(cos\left(y\right)\right)^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dt=cos(t)cos(y)^2. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the t variable to the right side of the equality. Simplify the expression \frac{1}{\cos\left(y\right)^2}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to t. Solve the integral \int\sec\left(y\right)^2dy and replace the result in the differential equation.
Solve the differential equation dy/dt=cos(t)cos(y)^2
Final answer to the exercise
$y=\arctan\left(\sin\left(t\right)+C_0\right)$