Question

how would i solve the differential equation

dx/dt=-kx^2

i.e. solve for x as a function of t.

I've been told to rearrange the equation to yield

dx/x^2=-k dt

but what can and should I do now?

Answer 1

integral of x^n dx = (1/(n+1)) x^(n+1) in general

integral of x^-2 dx = (1/-1) x^-1
which is( 1/x ) + constant of integration

the right side is -k t + constant of integration

1/x = -k t + c
x = 1/ (-kt+c)
undefined when kt = c