If y^2=a x^2+b x+c , where a, b, c are constants, then y^3 d^2 y d x^2 is equal to

Step-by-step solution

y^2=a x^2+b x+c Differentiating w.r.t. x , we get aligned & 2 y d y d x =2 a x+b 2 y d^2 y d x^2 +2 ( d y d x )^2=2 a & y d^2 y d x^2 + ( d y d x )^2=a & y^3 d^2 y d x^2 = (a x^2+b x+c ) [ ( 2 a x+b 2 )^2-a ] aligned R.H.S. of eq. (1) is a function of ' x ' only.