Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Morning ShiftMathematicsDifferential EquationsActual

The general solution of (1+e^ x y ) d x+e^ x y (1- x y ) d y=0 is

Options

  1. Ay e^ y x +x=c
  2. By e^ x y -x=c
  3. Cy e^ x y +y=c
  4. Dy e^ x y +x=c

Correct answer

D. y e^ x y +x=c

Step-by-step solution

Given, aligned & (1+e^ x / y ) d x+e^ x / y (1- x y ) d y=0 & (1+e^ x / y ) d x=-e^ x / y (1- x y ) d y & d x d y = -e^ x / y (1- x y ) (1+e^ x / y ) aligned Putting x=v y Differentiating w.r.t. y , aligned d x d y & =v d(y) d y +y d v d y d x d y & =v+y d v d y aligned Putting value of d x d y and x=v y in Eq. (i) aligned d y d x & = e^ -x / y (1- x y ) 1+e^ x / y v+y d v d y & = -e^v(1-v) 1+e^v y d v d y & =- e^v+v e^v 1+e^v -v y d v d y & = -e^v+v e^v-v-v e^v 1-e^v [ d v d y . & = - [v+e^v ] 1+e^v [ 1+e^v v+e^v

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 AP EAMCET PYQs