Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202522 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

The equation of the curve passing through (2, 9 2 ) and having the slope (1- 1 x^2 ) at ( x , y ) is

Options

  1. Ax y=x^2+2 x+1
  2. Bx y=x^2+x+2
  3. Cx y=x^2+x+5
  4. Dx y=x^2+2 x+5

Correct answer

A. x y=x^2+2 x+1

Step-by-step solution

The slope at any point (x, y) is dy dx = 1 - 1 x^2 . Integrating both sides with respect to x yields y = (1 - x⁻²)dx = x + x⁻¹ + C . Given that the curve passes through (2, 9 2 ) , substitute to find C : 9 2 = 2 + 1 2 + C C = 2 The equation becomes y = x + 1 x + 2 . Multiplying through by x gives xy = x^2 + 1 + 2x = x^2 + 2x + 1 , which corresponds to option A .

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