Second derivative of e^x minus e^x

[eagleswings]

Homework Statement

Show that y(t) = e^t is a solution of y'' - y = 0,

Homework Equations

integral of e^x dx = e^x +c
derivative of e^x = e^x

The Attempt at a Solution

set m = d(e^t)/dt, which also = e^t then dm = e^t

then d(m)/dt = e^t if y(t) = e^t is a solution
integrate both sides m= e^t +c
substitute e^t = e^t + c which is true for C = 0
not sure if it is that simple

 

[Dick]

It's even more simple than that. Put y=e^t. y'=e^t. y''=e^t. y''-y=e^t-e^t=0. You don't need to say much more than that.

 

[eagleswings]

Thanks Dick! sometimes it just helps to be able to ask someone else to look at it.