A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\]
B) \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\]
C) \[\frac{dy}{dx}=0\]
D) \[\frac{dx}{dy}=0\]
Correct Answer: A
Solution :
The general equation of all non-vertical lines in a plane is \[ax+by=1\], where \[b\ne 0\]. On differentiating, we get \[a+b\frac{dy}{dx}=0\] Again differentiating, \[b\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] which is the required differential equation.
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