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Question
If logy = tan–1 x, then show that `(1+x^2) (d^2y)/(dx^2) + (2x - 1) dy/dx = 0 .`
Solution
Here,
`log y = tan -1 x `
Differentiating w.r.t. x, we get
`1/y. dy/dx = 1/(1+x^2)`
⇒`(1+x^2) dy/dx = y`
⇒ `(1+x^2) (d^2y)/dx^2 +2xdy/dx = dy /dx `
⇒ `(1+x^2) (d^2y)/dx^2 +2xdy/dx - dy /dx = 0 `
⇒ `(1+x^2) (d^2y)/dx^2 + (2x - 1) dy /dx = 0`
Hence proved.
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