Hi

 

himanshu I think the question is wrong.

 

it should be   Prove that  d²y/dx²+(dy/dx)² * 1/y  = 0

 

instead of  d²y/dx²+(dy/dx)²  = 0 .

 

Then you proceed by my method and multiply by y to dy/dx and you find that its equal to second order derivative .  I'l show it clearly

y = sqrt(3x+2)

 

dy/dx =  3 /  2*sqrt(3x+2)

 

d²y/dx² = -9/(  4* (3x+20^3/2 )   

 

 d²y/dx²+(dy/dx)² *1/y  

                    =   -9/(  4* (3x+2) ^3/2 ) + (3 /  2*sqrt(3x+2))^2  * 1/(3x  +2)^1/2

                    =   -9/(  4* (3x+2) ^3/2 ) + 9 / 4* (3x+2) ( 3x+2)^1/2

                    =  0 .

Hope its clear now!

 

Cheers!