Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEST2024MathematicsDifferential Equations

Let f and g be two distinct solutions of the ordinary differential equation y^ +y=0 such that the function W defined by the determinant W(x)= | array cc f(x) & g(x) f^ (x) & g^ (x) array | is not identically zero. Then W satisfies

Options

  1. AW^ +W^ +W=0
  2. BW^ +W^ -W=0
  3. CW^ +W^ =0
  4. DW^ +W=0

Correct answer

C. W^ +W^ =0

Step-by-step solution

No solution available.

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 NEST PYQs