Question

Find the Orthogonal Trajectories of the the curve... y^2=kx^3

Answer 1

first differentiate the expretion:
2yy'=3kx^2
now substitute y'=-1/y':
-2y/y'=3kx^2
separate variables and integrate:
dy/2y=-(1/3k) x^-2
1/2Ln|y|=(1/3k)x^-1 + Ln C
y^(1/2)=Ce^1/(3kx)
y=Ce^2/(3kx)

Answer 2

Thanks! :D