Suppose y1(t) = t and y2(t) = e^-t are both solutions of the second order linear
equation
y'' + p(t) y' + q(t) y = 0:
All of the functions below are also solutions of the same equation, EXCEPT
(a) y = 0
(b) y = 5t - 2e^-t
(c) y = 9te^-t
(d) y = -10(pie) t

Question

Suppose y1(t) = t and y2(t) = e^-t are both solutions of the second order linear
equation
y'' + p(t) y' + q(t) y = 0:
All of the functions below are also solutions of the same equation, EXCEPT
(a) y = 0
(b) y = 5t - 2e^-t
(c) y = 9te^-t
(d) y = -10(pie) t

turingtest · Answer

which one is not a linear combination of the two given solutions y1 and y2 ???

anonymous · Answer

I think what it is asking is basically out of the 6 solutions given (y1, y2, and a,b,c,d), which 5 could be solutions of the given equation.

turingtest · Answer

yes, I know that.
you have the solution set: $y_1=t$ and $ y_2=e^{-t}$
do you know the superposition principle?

anonymous · Answer

y = C1y1 +C2y2

turingtest · Answer

right, so for example, b) is a solution because we can let c1=5 and c2=-2 and get that answer
which answer can we *not* do that with?

anonymous · Answer

Ahh wow it really is that easy? That would be c) then.

turingtest · Answer

yep :)

anonymous · Answer

Thanks!

turingtest · Answer

welcome!