The differential equation of the family of lines having $x$ - intercept ' $\mathrm{a}$ ' and $y$ - intercept…
The differential equation of the family of lines having $x$ - intercept ' $\mathrm{a}$ ' and
$y$ - intercept ' $\mathrm{b}$ ' is
$\frac{d^{2} y}{d x^{2}}=-1$
$\frac{d^{2} y}{d x^{2}}=10$
$\frac{d^{2} y}{d x^{2}}=1$
$\frac{d^{2} y}{d x^{2}}=0$
Solution
Equation of line having $x-$ intercept $a$ and $y$ intercept $b$ is $\frac{x}{a}+\frac{y}{b}=1$ i.e. $b x+a y=a b$ Differentiating w.r.t. x, we get
$\mathrm{b}+\mathrm{a} \frac{\mathrm{dy}}{\mathrm{dx}}=0 \Rightarrow \mathrm{a} \frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{b} \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-\mathrm{b}}{\mathrm{a}}$
Again differentiating w.r.t. $\mathrm{x}$, we get
$\frac{d^{2} y}{d x^{2}}=0$