Help me plz y'''+6y''+y'-34y=0 if y1=e^-4x

Question

Help me plz    y'''+6y''+y'-34y=0 if  y1=e^-4x

anonymous · Answer

What do you mean by y1? @RaphaTkt

anonymous · Answer

I want to know how to find the other two roots by the method of reducing job order

amistre64 · Answer

doesnt this have to do with a wronskian?  i tend to get the methods mixed up

anonymous · Answer

I say just find the two missing roots of ED

anonymous · Answer

$$y'''+6y''+y'-34y=0$$ The characteristic equation is $$r^3+6r^2+r-34=0$$ The given solution $y_1=e^{-4x}$ tells you that $r=-4$ is a root of the characteristic equation. This means that you can write the characteristic polynomial as $$(r+4)(r^2+\cdots)=0$$ To find the $r^2+\cdots$ part I think you'll have to do some long division: $$\frac{r^3+6r^2+r-34}{r+4}=r^2+2r-7-\frac{6}{r+4}$$ However, checking with WA, $r=-4$ is not an root of the polynomial: http://www.wolframalpha.com/input/?i=r%5E3%2B6r%5E2%2Br-34%3D0 In fact, the solution doesn't contain a term of only $e^{-4x}$: http://www.wolframalpha.com/input/?i=y%27%27%27%2B6y%27%27%2By%27-34y%3D0