Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2018MathematicsDifferential Equations

If y = tan - 1 ⁡ x 2 then x 2 + 1 2 d 2 y d x 2 + 2 x x 2 + 1 d y d x =

Options

  1. A4
  2. B2
  3. C1
  4. D0

Correct answer

B. 2

Step-by-step solution

y = ( tan − 1 x ) 2 d y d x = 2 tan − 1 ( x ) ( 1 + x 2 ) ( 1 + x 2 ) d y d x = 2 tan − 1 ( x ) ( 1 + x 2 ) d 2 y d x 2 + d y d x ( 2 x ) = 2 1 + x 2 ( 1 + x 2 ) 2 d 2 y d x 2 + 2 x ( x 2 + 1 ) d y d x = 2

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