dx/dt = (x+2) sin^2 2t, given x=0, t=0. Solve the differential equation and calculate value x when t= pie/4, giving your answer in 3 significant figures.
grrr. pi, not pie!
split it up and you have
dx/(x+2) = sin^2(2t) dt
ln(x+2) = 1/8 (4t-sin(4t))+c
x+2 = c e^(1/8 (4t-sin(4t))
at (0,0) we have
2 = c, so
x = 2e^(1/8 (4t-sin(4t)) - 2