Question

Which of the following differential equations has `y = x` as one of its particular solution?

Options

• `(d^2y)/(dx^2) - x^2  (dy)/(dx) + xy = x`

• `(d^2y)/(dx^2) - x  (dy)/(dx) + xy = x`

• `(d^2y)/(dx^2) - x^2  (dy)/(dx) + xy = 0`

• `(d^2y)/(dx^2) + x  (dy)/(dx) + xy = 0`

Answer 1

`(d^2y)/(dx^2) - x^2  (dy)/(dx) + xy = 0`

Explanation:

The curve is, `y = x`

Differentiating w.r.t. x.

`y^1 = 1` and `y^11 = 0`

Now consider part (c)d

= `(d^2y)/(dx^2) - x^2 (dy)/(dx) + xy = 0  x^2 * 1 + x * x`

∵ `y = x`

= `-x^2 + x^2`

= 0