Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2007MathematicsDifferential Equations

The solution of (x+y+1) d y d x =1 is

Options

  1. Ay=(x+2)+c e^x
  2. Bx=-(y+2)+c e^y
  3. Cx=-(y+2)+c e^y
  4. Dx=(y+2)^2+c e^y

Correct answer

C. x=-(y+2)+c e^y

Step-by-step solution

Given, (x+y+1) d y d x =1 d x d y =x+y+1 d x d y -x=y+1 , which is linear. aligned & IF =e^ -1 d y =e^ -y & Solution is x e^ -y = (y+1) e^ -y d y & x e^ -y = (y e^ -y +e^ -y ) d y+c & x e^ -y =-y e^ -y + 1 e^ -y d y+e^ -y (-1)+c & x e^ -y =-y e^ -y -e^ -y -e^ -y +c & x e^ -y =-(y+2) e^ -y +c & x=-(y+2)+c e^y 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 AP EAMCET PYQs