Answer to Question #124056 in Calculus for Desmond

Question

Verify that the given family of functions solves the differential equation.
i. dy/dt = (1 - 2t)y² , y = 1/( C - t + t²)
0
ⁱⁱ· dy/dt = y²sin(t) ,y = 1/(C + cos(t))

Answer 1

(i)

Y= 1/c-t+t²

dy/dt = (1-2t) y²

dy/dt =-1/(c-t+t²)² ×(-1+2t)

= (1-2t)×1/(c-t+t²)²

dy/dt =(1-2t)×y² => answer

(ii)

y = 1/(c+cost),

dy/dt= -1/(c+cost)²×(-sint),

dy/dt =(sint)y² => answer