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Question
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
Solution
Given, y = `sqrt(ax + b)`
Then, `dy/dx = a/(2sqrt(ax + b)`
`\implies dy/dx = a/(2y)`
`\implies y dy/dx = a/2`
Again, differentiating with respect to x, we get
`\implies y(d^2y)/(dx^2) + dy/dx xx dy/dx` = 0
`\implies y(d^2y)/(dx^2) + (dy/dx)^2` = 0
Hence Proved.
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