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Question
if `x = tan(1/a log y)`, prove that `(1+x^2) (d^2y)/(dx^2) + (2x + a) (dy)/(dx) = 0`
Solution
`x = tan (1/a log y)`
`:. 1/a log y = tan^(-1) x`
differentiating both sides w.r.t x
`y = e^(tan^(-1)x)`
`dy/dx = e^(atan^(-1)x).(a/(1+x^2))`
`(1+x^2) dy/dx = ay`
Again differentiating both sides w.r.t x
`(1+x^2) (d^2y)/(dx^2) + dy/dx^2. 2x = a dy/dx`
`(1+x^2) (d^2y)/(dx^2) + dy/dx (2x - a) = 0`
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