Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202618 April 2026Evening ShiftMathematicsDifferential EquationsActual

The differential equation of the family of all parabolas whose axis is the y -axis is

Options

  1. Ad^2y dx^2 + x dy dx = 0
  2. Bx d^2y dx^2 - dy dx = 0
  3. Cd^2y dx^2 - x dy dx = 0
  4. Dx d^2y dx^2 + dy dx = 0

Correct answer

B. x d^2y dx^2 - dy dx = 0

Step-by-step solution

The equation of the family of all parabolas whose axis is the y -axis is given by: y = ax^2 + c where a and c are arbitrary constants. Differentiating both sides with respect to x , we get: dy dx = 2ax 2a = 1 x dy dx Differentiating again with respect to x , we get: d^2y dx^2 = 2a Substituting the value of 2a from the first derivative into the second derivative, we get: d^2y dx^2 = 1 x dy dx x d^2y dx^2 - dy dx = 0 Answer: x d^2y dx^2 - dy dx = 0

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