Question

(D^4+6D^3+15D^2+20D+12)Y=0
higher order differential equation

Answer 1

@dan815

Answer 2

you can try y=e^(rx)
and solve the characteristic equation

Answer 3

Power series always works too

Answer 4

i was trying to take common out like this

Answer 5

uhhh

Answer 6

whats up with the 32

Answer 7

I think you should solve the characteristic equation

Answer 8

(D^4+6D^3+15D^2+20D+12)Y=0
Y=e^(rx)
e^(rx)(r^4+6*r^3+15*r^2+20r+12)=0

(r^4+6*r^3+15*r^2+20r+12)=0

solve for r

Answer 9

Is it a 32 or a 12? 0_o now I'm confused also

Answer 10

i think u added the 20 + 12 for some reason :P

Answer 11

yep i m trying i assumed r=-2 but not getting the answer even with -1 so that means r = 0

Answer 12

r=0 wont work since we have a constant in the characteristic equation

Answer 13

(r^4+6*r^3+15*r^2+20r+12)=0
try -4 and -3

Answer 14

-6 too

Answer 15

-4 IS WORKING

Answer 16

okay now use synthetic division and carry on

Answer 17

but in my book the first power is -2 why ?

Answer 18

then -2 works too

Answer 19

yeah.. i dunno you need to try these numbers out properly and factor it

Answer 20

wait let me try

Answer 21

Now i have D^2 +2D+3

Answer 22

@dan815

Answer 23

So you had a repeated root at -2 I guess? :)

Answer 24

\[\Large\rm D=\frac{-2\pm\sqrt{4-4(3)}}{2}\]I guess the last two roots are going to be complex, ya?

Answer 25

yep

Answer 26

i got 4 roots -2,-2,-3,-1

Answer 27

are they correct

Answer 28

-3 and -1 would give you -4D for the middle term, not 2D.
Those don't quite work out :(

Answer 29

No more real roots after your -2 and -2.
Have to use Quadratic Formula from here.

Answer 30

i used factorization

Answer 31

\[\Large\rm D=\frac{-2\pm\sqrt{-8}}{2}\]\[\Large\rm D=\frac{-2\pm2\sqrt{-2}}{2}\]\[\Large\rm D=-1\pm \sqrt2~i\]Ya these last two are complex roots :o
Remember what your y solutions will look like when you get complex roots to your characteristic? :)

Answer 32

..? :\

Answer 33

oops sorry
thanks for cleareing up the confusion

Answer 34

:3

Answer 35

in scientific calculator do we have a direct way solving Quadratic equation in similar way

Answer 36

Actually yes!
If you graph it, y=x^4+6x^3+15x^2+20x+12

You'll get a parabola shape like this.
https://www.desmos.com/calculator/9da3yxebbe

When looking for roots, you're really looking for where the line touches the x-axis.