Exercise
$\tan\:^2\left(y\right)dx=csc^3\left(x\right)dy$
Step-by-step Solution
Learn how to solve special products problems step by step online. Solve the differential equation tan(y)^2dx=csc(x)^3dy. 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{1}{\tan\left(y\right)^2}dy. Simplify the expression \frac{1}{\csc\left(x\right)^3}dx. 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 tan(y)^2dx=csc(x)^3dy
Final answer to the exercise
$-y-\cot\left(y\right)=\frac{-\sin\left(x\right)^{2}\cos\left(x\right)}{3}-\frac{2}{3}\cos\left(x\right)+C_0$