Question

State whether the following statement is true or false.

The integrating factor of the differential equation `(dy)/(dx) + y/x` = x³ is – x.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

`(dy)/(dx) + y/x` = x³ 

∴ `(dy)/(dx) + (x^-1). y = x^3`

Comparing with `(dy)/(dx) + Py = Q`, we get

P = x^–1, Q = x³

 Now, I.F. = `e^(intpdx)`

= `e^(intx^-1 dx)`

= `e^(logx)`

= x.