Question

\[f(x)= d^2 x/dt +5x\]

Answer 1

is it linear operation?

Answer 2

here's what I did, need confirmation

\[kf(x_1)+jf(x_2)=d^2 /dt (x_1 k + x_2 j)+ 5(x_1 k + x_2 j)\]

Answer 3

What does \(\frac{d^2x}{dt}\) mean?

Answer 4

\[kf(x_1)+jf(x_2)=k(d^2 x_1/dt + 5 x_1 )+ j(d^2 x_2/dt + 5 x_2 ))\]

Answer 5

not sure what you are doing with the k and j.

is this a non-homogeneous 2nd order DE?
is f(x) like y or can you treat it like x(t)

Answer 6

I am not trying to solve it, just checking linearity

Answer 7

oh ok,
yeah it seems to be linear.

can you just look at f'(x)
f'(x) = 5 implying a constant slope wrt x

Answer 8

oh okay, I will try that

Answer 9

i could be wrong though... i think it depends on what x(t) is since that will determine the behavior of d^2x/dt