Answer to Question #124134 in Differential Equations for Kofi

Question

Verify that the given family of functions solves the differential equation.
dy/dt = (1-2t) y² , y = 1 / (C - t + t² )

dy/dt = y² sin(t) , y = 1 / (C +cos(t))

Answer 1

$\dfrac{dy}{dt}=(1-2t)y^2\newline \dfrac{dy}{y^2}=(1-2t)*dt\newline \dfrac{-1}{y}=t-t^2-C\newline y=\dfrac{1}{(C-t+t^2)}\newline \dfrac{dy}{dt}=y^2*\sin{(t)}\newline \dfrac{dy}{y^2}=\sin{(t)}*dt\newline \dfrac{-1}{y}=-\cos{(t)}-C\newline y=\dfrac{1}{C+\cos{(t)}}$