# Search results

1. ### General solution to third order differential equation

yIII+yII-yI-y = 0 I used the characteristic equation and got: r3+r2-r = 0 r (r2+r-1) = 0 Which means that r = 0 is one root, And the other factors from the polynomial are (-1-Sqrt(5))/2 and (-1+Sqrt(5))/2 This means that the final answer would be: y = C1 Exp(0x) + C2 Exp((-1-Sqrt(5))/2) +...
2. ### Whats a non-trivial linear combination of these functions?

awesome thanks
3. ### Whats a non-trivial linear combination of these functions?

17sin2x+17cos2x? so C1 = 17Sin2x + 17Cos2x then just apply another coefficient to 2Sin2x, and 3Cos2x to make the new coefficient equal 17?
4. ### Whats a non-trivial linear combination of these functions?

I know that sin2x + cos2x = 1, and I've tried that, but im still not getting it C22Sin2(x)=-C33Cos2(x) C22(1-cos2(x))=-C33Cos2(x) C2(2-2cos2(x))=-C33cos2(x) but this doesnt simplify into a constant solution, as far as i worked it out
5. ### Whats a non-trivial linear combination of these functions?

I have to find a non-trivial, linear combination of the following functions that vanishes identically. In other words C1f + C2g + C3h = 0 Where C1, C2, and C3 are all constant, and cannot all = 0. f(x)=17 g(x)=2Sin2(x) h(x)=3Cos2(x) I figure C1 = 0, because there's really no constant...