Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20228 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

General solution of the differential equation x y ~d y= (x e ^x x+ e ^x ) d x is (where C is a constant of integration.)

Options

  1. Ay= e ^x x+C
  2. By= e ^x+C x
  3. Cy=C e ^x+ x
  4. De ^x y= x+C

Correct answer

A. y= e ^x x+C

Step-by-step solution

aligned & x y ~d y= (x e ^x x+ e ^x ) d x & y ~d y= e ^x x+ 1 x d x & y= e ^x x+C [ e ^x f(x)+f^ (x) d x= e ^x f(x)+C ] 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