Question

Choose the correct alternative.

The differential equation of `y = k_1e^x+ k_2 e^-x` is

Options

• `(d^2y)/dx^2 - y = 0`

• `(d^2y)/dx^2 + dy/dx  = 0`

• `(d^2y)/dx^2 + ydy/dx  = 0`*

• `(d^2y)/dx^2 + y  = 0`

Answer 1

The differential equation of `y = k_1e^x+ k_2 e^-x` is `(d^2y)/dx^2 - y = 0`

Explanation

`y = k_1e^x+ k_2 e^-x`

Differentiating w.r.t. x, we get

`dy/dx = k_1e^x -  k_2 e^-x`

Again, differentiating w.r.t. x, we get

`(d^2y)/dx^2 = k_1 e^x + k_2 e^-x`

∴ `(d^2y)/dx^2 = y`

∴ `(d^2y)/dx^2 - y = 0`