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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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The number of solutions of$\Large\frac{dy}{dx}=\Large\frac{y+1}{x-1}$ when y(1)=2 is\[(A)\;none\quad(B)\;one\quad(C)\;two\quad(D)\;infinite\]

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  • A linear differential equation of the form $\large\frac{dy}{dx}$$=f(x)$ can be solved by seperating the variables and then integrating it
Given $ \large\frac{dy}{dx}=\frac{y+1}{x-1}$
On seperating the variables we get,
$\large\frac{dy}{y+1}=\frac{dx}{x-1}$
integrating on both sides we get,
$\int \large\frac{dy}{y+1}=\int \frac{dx}{x-1}$
$=>\log (y+1)=\log (x-1)+\log c$
$=>\log (y+1)=\log c(x-1)$
Therefore $c(x-1)=(y+1)$
It is given $y(1)=2$=> when $x=1,y=2$
Now substituing the values for x and y
$c(1-1)=(2+1)$
$=>c=0$
Hence $(y+1)=(x-1)\;or\;x-y-2=0$ is the required solution
The number of solution is one
Hence $B$ is the correct option
answered May 16, 2013 by meena.p
 

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