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Form the differential equation of family of lines having intercepts a and b on the co-ordinate ares respectively.

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Solution

The equation of the line having intercepts a and b on the coordinate axes respectively, is

`"x"/"a" + "y"/"b" = 1`   ...(1)

where a and b are arbitrary constants.

Differentiating (1) w.r.t. x, we get

`1/"a" (1) + (1/"b") * "dy"/"dx" = 0`

∴ `(1/"b")"dy"/"dx" = - 1/"a"`

∴ `"dy"/"dx" = - "b"/"a"`

Differentiating again w.r.t. x, we get

`("d"^2"y")/"dx"^2 = 0`

This is the required D.E.

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Chapter 6: Differential Equations - Exercise 6.2 [Page 196]

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