(2x)d2t/dx2 - 6(dx/dt)^2 = x^2 - 3x^4

show that the substitution y=1/x^2 transforms this differential eqn into d2y/dt2 + y = 3

So i've work out

-2/x^3(d2x/dt2) + 6/x^4(dx/dt)

i think the latter part of this eqn is wrong as the mark scheme says it's 6/x^4(dx/dt)^2

Can anyone explain this?