Question

Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for the solution.

By' +y=0; y e-x/8
When y = e-x/8,
y'--8
Thus, in terms of x,
Sy' + y =
0
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X +ex/8

Answer 1

We have the DE,
`y'+y=0`, verify that
`y=e^{(-x)/(8)}` is a solution.

We have,
`y=e^{(-x)/(8)}`, find
`y'`.

=>
`y'=(-1)/(8) e^{(-x)/(8)}`

Plug
`y` and
`y'` into the DE.

=>
`y'+y=0`

=>
`((-1)/(8) e^{(-x)/(8)})+(e^{(-x)/(8)})=0`

=>
`e^{(-x)/(8)}=(1)/(8) e^{(-x)/(8)}`

=>
`e^{(-x)/(8)}\\eq (1)/(8) e^{(-x)/(8)}`

Thus,
`y=e^{(-x)/(8)}`, is not a solution to the given DE.