A) \[(x+1)\frac{dy}{dx}-y=0\]
B) \[(x+1)\frac{dy}{dx}+y=0\]
C) \[\frac{dy}{dx}=\frac{x-1}{y-1}\]
D) \[\frac{dy}{dx}=\frac{x+1}{y+1}\]
Correct Answer: A
Solution :
Equation of line whose slope is equal to y intercept, is \[y=cx+c=c(x+1)\] ...(i) \[\Rightarrow \] \[\frac{dy}{dx}=c\] ?..(ii) On putting the value of c from Eq. (i) in Eq. (ii), we get \[\frac{dy}{dx}=\frac{y}{x+1}\] \[\Rightarrow \] \[(x+1)\frac{dy}{dx}-y=0\] Which is the required differential equation.
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