A) \[x\frac{dy}{dx}+y=0\]
B) \[x+\frac{dy}{dx}=0\]
C) \[\frac{dy}{dx}=y\]
D) \[\frac{dy}{dx}=x\]
E) \[x\frac{dy}{dx}-y=0\]
Correct Answer: E
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)) \[\Rightarrow \] \[x\frac{dy}{dx}-y=0\]You need to login to perform this action.
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