Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202313 May 2023Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation e ^ -x (y+1) d y+ ( ^2 x- 2 x ) y ~d x=0 at x=0 , y=1 is

Options

  1. A(y+1)+ e ^x ^2 x=2
  2. By+ y= e ^x ^2 x
  3. C(y+1)+ e ^x ^2 x=1
  4. Dy+ y+ e ^x ^2 x=2

Correct answer

D. y+ y+ e ^x ^2 x=2

Step-by-step solution

aligned & e ^ -x (y+1) d y+ ( ^2 x- 2 x ) y ~d x=0 & y+1 y ~d y+ e ^x ( ^2 x- 2 x ) d x=0 aligned Integrating on both sides, we get aligned & (1+ 1 y ) d y+ e ^x ( ^2 x-2 x x ) d x= c & y+ |y|+ e ^x ^2 x= c & At x=0, y=1 & 1+ 1+ e ^0 ^2 0= c & c =2 & y+ |y|+ e ^x ^2 x=2 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 MHT CET PYQs