Question

x''=(x')^2 how can you reduce to a first order diff eq?

Answer 1

x'' (t) - x' ^2 = 0

Answer 2

so is that separable to y=-1/(x+C1) ?

Answer 3

not sure, one sec

Answer 4

let x'(t) = v(t)

Answer 5

let start over
x''(t) = x'(t)^2

Answer 6

if x'(t) = v(t), then x''(t) = v'(t)

Answer 7

now we have
v'(t) = v(t)^2, which is first order

Answer 8

right so it would be v'(t)+v(t)^2=0

Answer 9

minus

Answer 10

how about we divide both sides by v(t)^2