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Mathematics
The differential equation of the family of lines passing through the origin is:
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Q. The differential equation of the family of lines passing through the origin is:
KEAM
KEAM 2002
A
$ x\frac{dy}{dx}+y=0 $
B
$ x+\frac{dy}{dx}=0 $
C
$ \frac{dy}{dx}=y $
D
$ \frac{dy}{dx}=x $
E
$ x\frac{dy}{dx}-y=0 $
Solution:
The equation of line passing through the origin is given by $ y=mx $ ...(i) On differentiating w.r.t. $ x, $ we get $ \frac{dy}{dx}=m $ $ \Rightarrow $ $ \frac{dy}{dx}=\frac{y}{x} $ (using Eq. (i)) $ \Rightarrow $ $ x\frac{dy}{dx}-y=0 $