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Need solution for RD Sharma maths class 12 chapter 21 Differential Equation exercise Fill in the blank question 23

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 \frac{\mathrm{d} ^{2}x}{\mathrm{d} y^{2}}=0


The differential equation of all non-horizontal lines in a plane is ____


 y=mx+c \quad (m=slope)


Equation of non-horizontal line in a plane is y = mx + c where ‘m’ is slope.

Since, there are two arbitrary constants. so the order will be two hence we can differentiate the equation of line two times.

Differentiate w.r.t x

\begin{aligned} &\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}=m \\ &\Rightarrow \frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=0 \end{aligned}

So, the answer is

\begin{aligned} & \frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}=0 \end{aligned}

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Gurleen Kaur

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