## anonymous 4 years ago $f(x)= d^2 x/dt +5x$

1. anonymous

is it linear operation?

2. anonymous

here's what I did, need confirmation $kf(x_1)+jf(x_2)=d^2 /dt (x_1 k + x_2 j)+ 5(x_1 k + x_2 j)$

3. Mr.Math

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

4. anonymous

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

5. anonymous

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)

6. anonymous

I am not trying to solve it, just checking linearity

7. anonymous

oh ok, yeah it seems to be linear. can you just look at f'(x) f'(x) = 5 implying a constant slope wrt x

8. anonymous

oh okay, I will try that

9. anonymous

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