Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202314 May 2023Evening ShiftMathematicsDifferential EquationsActual

The differential equation representing the family of curves y^2=2 c (x+ c ) , where c is a positive parameter, is of

Options

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

Correct answer

D. order 1, degree 3

Step-by-step solution

y^2=2 c (x+ c )... (i) Differentiating w.r.t. x , we get 2 y d y ~d x =2 c ... (ii) Substituting (ii) in (i), we get aligned & y^2=2 y d y ~d x (x+ y d y ~d x ) & y=2 x d y ~d x +2 d y ~d x y d y ~d x & (y-2 x d y ~d x )^2=4 y ( d y ~d x )^3 aligned This is a differential equation of order 1 and degree 3 .

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All MHT CET PYQs