Exercise
$\sin\:\left(x\right)\cos\:^2\left(y\right)-\cos\:\left(x\right)\sin\:\left(y\right)y'\:=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation sin(x)cos(y)^2-cos(x)sin(y)y^'=0. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting \sin\left(x\right)\cos\left(y\right)^2 from both sides of the equation. Multiply both sides of the equation by -1. Multiply -1 times -1.
Solve the differential equation sin(x)cos(y)^2-cos(x)sin(y)y^'=0
Final answer to the exercise
$y=\mathrm{arcsec}\left(-\ln\left(\cos\left(x\right)\right)+C_0\right)$