Question

SOLVE THE GIVEN DIFFERENTIAL EQUATION BY SEPARATION OF VARIABLES
DY/DX=Y-2/X-1
Y(2)=2

Answer 1

Here the problem is written in lower case.

$\frac{dy}{dx}= \frac{y-2}{x-1}$

=> $\frac{dy}{y-2}= \frac{dx}{x-1}$

Integrating we get

$\int\frac{dy}{y-2}=\int \frac{dx}{x-1}$

ln|y-2| = ln|x-1| + ln|C|

=> ln|y-2| = ln|C(x-1)|

=>| y - 2 |= |C(x-1)|

By initial condition , y = 2 when x = 2

0 = |C| i.e C = 0

Therefore the particular solution is

|y - 2| = 0

i.e. y= 2