Question

solve differential equation dy/dt=-4y^3 y(0)=2.5

Answer 1

separable differential equation,
dy/y^3 = -4 dt
integrate bothside
-1/(2y^2) = -4t + c
algebra.
y(t)^2 = 1/(8t-2c)
use initial condition y(0)=2.5
2.5^2 =1/(-2c)
25/4 = 1/ -2c
-2/25 = c

so your solution is
y(t)^2 = 1/ (8t + 4/25)

you can move the square around and make the solution y(t) = +/- 1/sqrt(8t + 4/25)

Answer 2

Why is 2C not absorbed to C?

Answer 3

I could do that, i would still get the same answer.

Answer 4

y(t)^2 = 1/(8t+c)
use initial condition y(0)=2.5
2.5^2 =1/(c)
25/4 = 1/ c
4/25 = c

Answer 5

that's when you absorb -2 into the C