Exercise
$\frac{dy}{dt}\sec\left(t\right)=\frac{-y^3}{2}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dtsec(t)=(-y^3)/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{2}{-y^3}dy. Simplify the expression \frac{1}{\sec\left(t\right)}dt. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to t.
Solve the differential equation dy/dtsec(t)=(-y^3)/2
Final answer to the exercise
$y=\frac{1}{\sqrt{\sin\left(t\right)+C_0}},\:y=\frac{-1}{\sqrt{\sin\left(t\right)+C_0}}$