Question

Find the solution of the Diffrential Equation
dy/dt = -| tan^5(y) |

Answer 1

well, the absolute value looks a bit weird.

break it up into two eqns , one when tan^5(y) >= 0 , so that will mean that |tan^5(y)| = tan^5(y)

and one when tan^5(y)<0

Answer 2

so first case :

dy/dt = - tan^5 (y) --> separate

dy/ tan^5 (y) = -dt

sec^5(y) dy = - dt --> now integrate

break LHS into sec^4 and sec

remember that sin^2 +cos^2 =1 , so sec^2 = 1 + tan^2