The solution of the equation y e-x / y d x-(x e-x / y+y3) d y=0 is

Question

The solution of the equation y e-x / y d x-(x e-x / y+y3) d y=0 is (A) 3 e-x / y+y2=c (B) 2 e-x / y+y2=c (C) 2 ex / y+y2=c (D) None of these

Tardigrade Admin · Accepted Answer

The given equation can be written as (y d x-x d y) e-x / y-y3 d y=0 ⇒ (y d x-x d y/y2) e-x / y=y d y ⇒ d(x / y) e-x / y=y d y On integrating, we get -e-x / y=(y2/2)+c or, 2 e-x / y+y2=c

Q. The solution of the equation $y e^{- x / y} d x - (x e^{- x / y} + y^{3})$ $d y = 0$ is

$3 e^{- x / y} + y^{2} = c$

$2 e^{- x / y} + y^{2} = c$

$2 e^{- x / y} + y^{2} = c$

None of these

The given equation can be written as
$(y d x - x d y) e^{- x / y} - y^{3} d y = 0$
$\Rightarrow \frac{y d x - x d y}{y ^{2}} e^{- x / y} = y d y$
$\Rightarrow d (x / y) e^{- x / y} = y d y$
On integrating, we get
$- e^{- x / y} = \frac{y ^{2}}{2} + c$
or, $2 e^{- x / y} + y^{2} = c$

Q. The solution of the equation ye−x/ydx−(xe−x/y+y3) dy=0 is

3e−x/y+y2=c

2e−x/y+y2=c

2e−x/y+y2=c

None of these

The given equation can be written as (ydx−xdy)e−x/y−y3dy=0 ⇒y2ydx−xdy​e−x/y=ydy ⇒d(x/y)e−x/y=ydy On integrating, we get −e−x/y=2y2​+c or, 2e−x/y+y2=c

Q. The solution of the equation $y e^{- x / y} d x - (x e^{- x / y} + y^{3})$ $d y = 0$ is

$3 e^{- x / y} + y^{2} = c$

$2 e^{- x / y} + y^{2} = c$

$2 e^{- x / y} + y^{2} = c$

The given equation can be written as
$(y d x - x d y) e^{- x / y} - y^{3} d y = 0$
$\Rightarrow \frac{y d x - x d y}{y ^{2}} e^{- x / y} = y d y$
$\Rightarrow d (x / y) e^{- x / y} = y d y$
On integrating, we get
$- e^{- x / y} = \frac{y ^{2}}{2} + c$
or, $2 e^{- x / y} + y^{2} = c$