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Question
Obtain the differential equations by eliminating arbitrary constants from the following equation.
`y = c_2 + c_1/x`
Solution
`y = c_2 + c_1/x`
Differentiating w.r.t. x, we get
`dy/dx = (-c_1)/x^2`
∴ `x^2dy/dx = - c_1`
Again, differentiating w.r.t. x, we get
`x^2 (d^2y)/dx^2 + dy/dx. 2x = 0`
∴ `x^2 (d^2y)/dx^2 + 2x dy/dx = 0`
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