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Question
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
Options
`(d^2y)/dx^2 + 2 dy/dx = 0`
`x(d^2y)/dx^2 + 2 dy/dx = 0`
`(d^2y)/dx^2 -2 dy/dx = 0`
`x(d^2y)/dx^2 -2 dy/dx = 0`
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Solution
The differential equation of `y = k_1 + k_2/x` is `x(d^2y)/dx^2 + 2 dy/dx = 0`
Explanation
`y = k_1 + k_2/x`
∴ xy = xk1 + k2
Differentiating w.r.t. x, we get
`y+x dy/dx = k_1`
Again, differentiating w.r.t. x, we get
`dy/dx + dy/dx + x (d^2y)/dx^2 = 0`
∴ `x (d^2y)/dx^2 + 2 dy/dx = 0`
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