Question

dx/dy=u , d2x/dy2=v s.t. d2y/dx2=-v/u please solve this problem?

Answer 1

dx/dy = u       d²x/dy² = v              d²y/dx² =  - v/u
v is also = du/dy

dy/dx = 1/u
 =>  d²y/dx² = -1/u²  * du/dx
                   = -1/u² * du/dy * dy/dx
                   = -1/u² * v * 1/u  = -v /u³

Comparing with given equation,  we get  u² = 1
     u = +1 or -1

Hence,    dy/dx = 1  or  -1
            y = x + K    or    y = K - x
            u = 1 or    -1 ,   
            v = 0