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प्रश्न
Obtain the differential equation by eliminating arbitrary constants from the following equation:
y = Ae3x + Be–3x
Find the differential equation by eliminating arbitrary constants from the relation y = Ae3x + Be−3x.
उत्तर
y = Ae3x + Be–3x ...(i)
Differentiating w.r.t. x, we get
`(dy)/(dx)` = Ae3x × 3 + Be–3x × (–3)
= 3Ae3x – 3Be–3x
and `(d^2y)/(dx^2)` = 3Ae3x × 3 – 3Be–3x × (–3)
= 9Ae3x + 9Be–3
= 9(Ae3x + 9Be–3)
= 9y ...[From (i)]
∴ `(d^2y)/(dx^2)` = 9y
This is the required differential equation.
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