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`

Answer 1

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`