The differential equation of the family of li | vedclass

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(A) The equation of a line with $x$-intercept $a$ and $y$-intercept $b$ is given by $\frac{x}{a} + \frac{y}{b} = 1$. Since there are two arbitrary con

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

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(A) The equation of a line with $x$-intercept $a$ and $y$-intercept $b$ is given by $\frac{x}{a} + \frac{y}{b} = 1$. Since there are two arbitrary constants $a$ and $b$,we differentiate the equation twice. Differentiating with respect to $x$: $\frac{1}{a} + \frac{1}{b} \frac{d y}{d x} = 0$ Differentiating again with respect to $x$: $0 + \frac{1}{b} \frac{d^2 y}{d x^2} = 0$ Since $b 
eq 0$,we have $\frac{d^2 y}{d x^2} = 0$.

The differential equation of the family of lines having $x$-intercept as $a$ and $y$-intercept as $b$ is:

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