Question

Form a differential equation if `y=e^x`?

Answer 1

We seek a differential equation with solution `y=e^x`

There are infinitely many such equations.

Noting that `AA n in NN`, then `y^((n))=e^x`, we can form some sample equations as follows,

`y'=y`

`y''-y = 0`

`y'''-y = 0`

`y''+y = 2e^x`

`vdots`