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Home  >>  CBSE XII  >>  Math  >>  Differential Equations

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $\large\frac{x}{a}+\frac{y}{b}=1$

$\begin{array}{1 1} (A)\;y'' = 0 \\(B)\;y' = 0 \\ (C)\;xy'' = 0 \\ (D)\;y''' = 0 \end{array} $

1 Answer

Toolbox:
  • Differentiation of $\large\frac{x}{a}$ is $\large\frac{1}{a}$
  • Differentiation of $\large\frac{y}{b}$ is $\large\frac{y'}{b}$
Step 1:
Given :$\large\frac{x}{a} +\frac{ y}{b}$$ = 1$
Differentiating on both sides we get,
$\large\frac{1}{a }+ \frac{y'}{b}$$ = 0$
Step 2:
Again differentiating we get
$0 + [\large\frac{1}{b}]$$y'' = 0$
$y'' = 0$
This is the required solution.
answered Aug 16, 2013 by sreemathi.v
 

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