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Questions  >>  CBSE XII  >>  Math  >>  Differential Equations
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Q)

Find the differential equation of all non vertical lines in a plane.

$\begin{array}{1 1}(A)\;\large\frac{d^2y}{dx^2}=\frac{dy}{dx} \\(B)\;\large\frac{d^2y}{dx^2}-y=0 \\(C)\;\large\frac{d^2y}{dx^2}=0 \\ (D)\;\large\frac{d^2y}{dx^2}-\frac{dy}{dx}-y=0\end{array} $

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A)
Toolbox:
  • A differential equation is a linear differential equation if it is expressible in the form : $ P_0 \Large\frac{d^ny}{dx^n}$$+P_1 \Large\frac{d^{n-1}y}{dx^{n-1}}$$+P_2\Large \frac{d^{n-2}y}{dx^{n-2}}$$+...P_n y=Q$ Where $P_0,P_1....P_n$ and $Q$ are constants or function independent of variable x
To find the differential equation of all non-vertical lines in a plane
Clearly the equation of non vertical line in a plane is
$y=mx+c$
differentiating with respect to x on both sides
$\large\frac{dy}{dx}$$=m$
again differentiating with respect to x on both sides
$\large\frac{d^2y}{dx^2}$$=0$
Hence the differential equation is
$\large\frac{d^2y}{dx^2}$$=0$
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