Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2023MathematicsDifferential Equations

If y=a x+b x , then y^2+ ( d y d x )^2 is a

Options

  1. Afunction of y
  2. Bfunction of x and y
  3. Cconstant
  4. Dfunction of x

Correct answer

C. constant

Step-by-step solution

Given, y=a x+b x aligned & d y d y =a x-b x & aligned y^2+ ( d y d x )^2=(a x+b x)^2 +(a x-b x)^2 aligned aligned aligned & =a^2 ^2 x+b^2 ^2 x+2 a b x & x+a^2 ^2 x+b^2 ^2 x-2 a b x x & =a^2 ( ^2 x+ ^2 x )+b^2 ( ^2 x+ ^2 x ) & =a^2+b^2 [ ^2 x+ ^2 x=1 ] & = constant aligned

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 KCET PYQs