Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202121 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation. ( y x ) ( y x ) d x- [ ( x y ) ( y x )+ ( y x ) ] d y=0 is

Options

  1. Ay ^2 ( y x )= k
  2. Bx ( y x )= k
  3. C( y x )= k
  4. Dy ( y x )=k

Correct answer

D. y ( y x )=k

Step-by-step solution

We have ( y x ) ( y x ) d x- [ ( x y ) ( y x )+ ( y x ) ] d y=0 d y d x = ( y x ) ( y x ) ( x y ) ( y x )+ ( y x ) Put y x =v y=v x d y d x =v+x d v d x aligned & v + x dv dx = v v 1 v v + v = v ^2 v v + v v x dy dx = - v v v + v v & v + v v v v dv = - dx x 1 v dv + v d v =- dx x & | v |+ |+ x |=- | x |+ k |( v )( v )( x )| & = k aligned y ( y x )=k

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