The solution to the differential equation ( dy / dx ) ln x +( y / x )=( dy / dx ) which passes through the point ( e 2, 3) is

Question

The solution to the differential equation ( dy / dx ) ln x +( y / x )=( dy / dx ) which passes through the point ( e 2, 3) is (A) y=3 ex-(3 ee2-3) (B) y =3 ln x -3 (C) y =(3/ ln x -1) (D) y=(9/1+ ln x)

Tardigrade Admin · Accepted Answer

( dy / dx ) ln x +( y / x )=( dy / dx ) ( d / dx )( y ln x )=( dy / dx ) text Integrating y ln x = y + C text Pass ( e 2, 3) 3 ⋅ 2=3+ C ⇒ C =3 y ln x = y +3 y =(3/ ln x -1) ⋅

Q. The solution to the differential equation $\frac{d y}{d x} ln x + \frac{y}{x} = \frac{d y}{d x}$ which passes through the point $(e^{2}, 3)$ is

$y = 3 e^{x} - (3 e^{e^{2}} - 3)$

$y = 3 ln x - 3$

$y = \frac{3}{l n x - 1}$

$y = \frac{9}{1 + l n x}$

$\frac{d y}{d x} ln x + \frac{y}{x} = \frac{d y}{d x}$
$\frac{d}{d x} (y ln x) = \frac{d y}{d x}$
$Integrating$
$y ln x = y + C Pass (e^{2}, 3)$
$3 \cdot 2 = 3 + C \Rightarrow C = 3$
$y ln x = y + 3$
$y = \frac{3}{l n x - 1} \cdot$

Q. The solution to the differential equation dxdy​lnx+xy​=dxdy​ which passes through the point (e2,3) is

y=3ex−(3ee2−3)

y=3lnx−3

y=lnx−13​

y=1+lnx9​