If y = etan^-1 x, show that (1 + x2) y” + (2x – 1) y’ = 0 – InterviewSolution

InterviewSolution

1.

If y = etan^-1 x, show that (1 + x2) y” + (2x – 1) y’ = 0

Answer»

y = e^{tan^-1 x}

y = e^{tan^-1 x} 1/(1 + x²)

⇒ y’ = y/(1 + x²) ⇒ y'(1 + x²) = y

Differentiating w.r.to x

y’ (2x) + (1 + x²) (y”) = y’

(i.e.) (1 + x²) y” + y’ (2x) – y’ = 0

(i.e.) (1 + x²) y” + (2x – 1) y’ = 0

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