Solve the differential equation dx/dt = 9x^4, and find the particular solution satisfying the initial condition x(0)=1/2. x(t)=

Answer 1

We separate variables and integrate: dx/x⁴ = 9dt; ∫x^-4dx = ∫9dt; -x^-3/3 = 9t + C; or - 1/x³ = 27t + 3C;

If t = 0 x(0) = 1/2, so, - 8 = 3C; C = - 8/3

1/x³ = 8 - 27t; x³ = 1/(8 - 27t); x(t) = (8 - 27t)^-1/3