Question

Solve the following separable ODE y^1=sec^2y

Answer 1

\[y'=\sec^2(y) \\ \frac{dy}{dx}=\sec^2(y) \\ \frac{dy}{\sec^2(y)}=dx \\ \cos^2(y) dy=dx\]
integrate both sides

Answer 2

Solve the following separable ODE xy^1 + y = 0, y(4) = 6

Answer 3

separate the variables again
subtract y on both sides then divide both sides by x and y
and multiply dx on both sides