Question

The differential equation for a²y = log x + b, is ______.

Options

• `x (d^2y)/(dx^2) - dy/dx` = 0

• `(d^2y)/(dx^2) - x dy/dx` = 0

• `x (d^2y)/(dx^2) + x^2 dy/dx` = 0

• `x (d^2y)/(dx^2) + dy/dx` = 0

Answer 1

The differential equation for a²y = log x + b, is `underlinebb(x (d^2y)/(dx^2) + dy/dx = 0)`.

Explanation:

a²y = log x + b

Differentiate w.r.t.x

`a^2 dy/dx = 1/x`   ....(1)

Again differentiate w.r.t.x

`a^2 (d^2y)/(dx^2) = - 1/x^2`    ....(2)

From (1): a² = `1/(x dy/dx)`

From (2): `1/(x dy/dx)*(d^2y)/(dx^2) = -1/x^2`

∴ `x(d^2y)/(dx^2) = -dy/dx`, etc.