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The differential equation representing the family of curves y^2=2 c(x+ c ) , where c>0 , is a parameter, is of order and degree as follows:

Options

  1. Aorder 1 , degree 2
  2. Border 1, degree 1
  3. Corder 1, degree 3
  4. Dorder 2, degree 2

Correct answer

C. order 1, degree 3

Step-by-step solution

aligned & y^2=2 c(x+ c ) .....(i) & 2 y y^ =2 c 1 or y y^ =c ....(ii) & y^2=2 y y^ (x+ y y^ ) aligned [on putting value of c from (ii) in (i)] On simplifying, we get (y-2 x y^ )^2=4 y y^ 3 .....(iii) Hence equation (iii) is of order 1 and degree 3.

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