AP EAMCET202422 May 2024Morning ShiftMathematicsDifferential EquationsActual
The general solution of the differential equation (1+ y)(d y-d x)+2 x d y=0 is
Options
- Ae^ x (y x+ x)+ x=c
- Be^ x (y x+ y x- x)+ x=0
- Ce^y(x y+x y- y)=c
- De^y(x y+x y+ y)=c
Correct answer
C. e^y(x y+x y- y)=c
Step-by-step solution
aligned & (1+ y)(d x-d y)+2 x d y=0 & d x d y + 2 x 1+ y =1 & I.F. =e^ 2 1+ y d y =e^ y+ ( y+ y) & =e^y( y+ y) aligned Solution is gathered x e^y( y+ y)= e^y( y+ y) d y+c x e^y( y+ y)=e^y y+c e^y(x y+x y- y)=c gathered