Find values of the real constants a, b and c for which x(t) = (at^b − c)^1/2 is a solution of the ODE

x.d2x/dt2 + (dx/dt)^2 = 1

and give the t-interval in which this expression is a solution for those values of the constants. Does anyoneknow how to begin this? =[

i tried finding x'(t), x''(t) and substitute..didnt work..

how would i find a,b,c?thank you!