Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202120 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

The general solution of (x d y d x -y ) y x =x^3 e^x is

Options

  1. Ae ^ x ( x -1)+ y x + c =0
  2. Bxe ^ x + y x + c =0
  3. Ce ^ x ( x +1)+ y x + c =0
  4. Dex ^ x - y x + c =0

Correct answer

A. e ^ x ( x -1)+ y x + c =0

Step-by-step solution

aligned & (x d y d x -y ) y x =x^3 e^x & Put y x =t x d y d x -y x^2 = d t d x aligned Put y x =t x d y d x -y x^2 = d t d x Hence eq. (i) becomes aligned & x ^2 ( d t d x ) t=x^3 e^x ( d t d x ) t=x e^x & t d t= x^x d x & - t=x e^x- e^x d x=x e^4-e^x+c & - ( y x )=e^x(x-1)+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