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

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

Mathematics
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is it linear operation?
here's what I did, need confirmation \[kf(x_1)+jf(x_2)=d^2 /dt (x_1 k + x_2 j)+ 5(x_1 k + x_2 j)\]
What does \(\frac{d^2x}{dt}\) mean?

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\[kf(x_1)+jf(x_2)=k(d^2 x_1/dt + 5 x_1 )+ j(d^2 x_2/dt + 5 x_2 ))\]
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)
I am not trying to solve it, just checking linearity
oh ok, yeah it seems to be linear. can you just look at f'(x) f'(x) = 5 implying a constant slope wrt x
oh okay, I will try that
i could be wrong though... i think it depends on what x(t) is since that will determine the behavior of d^2x/dt

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