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If m and n are respectively the order and the degree of the differential equation representing the family of curves y^2-5 a x-5 a^ 3 2 =0(a>0 is a parameter ) , then the value of m-n is

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

D. -2

Step-by-step solution

Given family of curves is now differentiating w.r.t. x2 y y^ -5 a=0 Putting value of a in equation (i) aligned & y^2-5 ( 2 5 y y^ ) x-5 ( 2 5 y y^ )^ 3 2 =0 & y^2-2 y y^ x=5 ( 2 5 y y^ )^ 3 2 aligned squarring both side aligned & ( y ^2-2 yy ^ x )^2=5^2 ( 2 5 yy ^ )^3 & m =1, n =3 & ~m - n =-2 aligned

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