Question

Solve the separable differential equation: dy/dt=4y^6
and find the particular solution satisfying the initial condition y(0)=-3

y(t)=?

Answer 1

Integral of dt = Integral of (1/4)y^-6 dy

t = -1/(20 y^-5) + C

0 = 1/20*243 +C

t = -1/(20 y^-5) -1/4860

1/(20 y^-5) = -(1/4860) - t

y^5 = (1/20)/[(-1/4860) - t]
= 243/[-1 -4860 t]
y = -3*[1 +4860 t]^(1/5)