I have a 2nd order ODE of general form:

y= Ae^(17x) + Be^(-x)

Initial conditions are:

y(0)=0; and

y'(0)=2

From this I got A = 1/9 and B= -1/9

Leading to:

1/9e^(17x) - 1/9e^(-x)

Even I can see the second term is tending to zero - as it was when I tested a few points.

In the question the instructions were:

"Find (if possible) the general solution to each of the following 2nd-order ODE by trying y=e^(landa x). If you can't give a solution, give a reason.

(a) y''+4y'+25y = 0

(b) y''-16y'-17y = 0; subject to y(0) = 0 and y'(0)=2"

Therefore I assume there is something unsolvable - do you think that would refer to not having initial conditions for part (a) or have something to do with the second half of the equation for (a) tending to zero?

For part (a) there were 2 complex roots but I thought that still meant it was solvable and at our level we are given the trig equation to substitute the values into - so I can't work out what might have gone wrong there.

I am just a bit confused as both seemed solvable yet the caveat in the question re not being able to find an solution leads me to think there is something more to this.

Kind regards

Beetle