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

The differential equation of family of lines, having $x$-intercept as a and $y$-intercept as $b$, is
  1. $\frac{d^2 y}{d x^2}=0$
  2. $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-\frac{\mathrm{d} y}{\mathrm{~d} x}+y=0$
  3. $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+\frac{\mathrm{d} y}{\mathrm{~d} x}=y$
  4. $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+\frac{\mathrm{d} y}{\mathrm{~d} x}=0$

Solution

Diff $\frac{x}{a}+\frac{y}{b}=1$ [two arbitrary constants] $\frac{1}{a}+\frac{1}{b} \cdot \frac{\mathrm{d} y}{\mathrm{~d} x}=0$ Again in diff $0+\frac{1}{b} \cdot \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=0$ $\Rightarrow \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=0$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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