The solution of the differential equation (dy/dx) = xex-y is

Question

The solution of the differential equation (dy/dx) = xex-y is (A) ex-y = c (B) ey (xex + ex) + c + 1 = 0 (C) ex-y = exy (D) none of these

Tardigrade Admin · Accepted Answer

(dy/dx) =xex-y=xex.e-y ey dy = xex dx Integrating both sides , we get ∫ eydy = ∫ xex dx + c ⇒ ey =xex - ∫1 . exdx + c ⇒ ey =xex -ex+c ⇒ ey -ex(x-1)+c =0

Q. The solution of the differential equation $\frac{d y}{d x} = x e^{x - y}$ is

$e^{x - y} = c$

$e^{y} (x e^{x} + e^{x}) + c + 1 = 0$

$e^{x - y} = e^{x y}$

none of these

$\frac{d y}{d x} = x e^{x - y} = x e^{x} . e^{- y}$
$e^{y} d y = x e^{x} d x$
Integrating both sides , we get
$\int e^{y} d y = \int x e^{x} d x + c$
$\Rightarrow e^{y} = x e^{x} - \int 1. e^{x} d x + c$
$\Rightarrow e^{y} = x e^{x} - e^{x} + c$
$\Rightarrow e^{y} - e^{x} (x - 1) + c = 0$

Q. The solution of the differential equation dxdy​=xex−y is

ex−y=c

ey(xex+ex)+c+1=0

ex−y=exy