Let y′′−3y′−40y=0

Question

Let y′′−3y′−40y=0

+3

3608

9

+102

Entered	Answer Preview	Result	Messages
(r^2)[e^(rx)]-3r[e^(rx)]-40[e^(r*x)]	r^2e^(rx)-3re^(rx)-40e^(rx)	correct
(e^rx)[(r-8)(r+5)]		incorrect	Powers must be either 0 or 1
-5, 8	−5,8	correct

At least one of the answers above is NOT correct.

(1 pt) Let y′′−3y′−40y=0.

Try a solution of the form y=erx, for some unknown constant r, by substituting it into the differential equation.
r^2*e^(rx)-3*r*e^(rx)-40*e^(rx)=0.
Simplify and factor your equation in the previous part as much as possible. Be sure to divide out any factors guaranteed to be nonzero.
______________=0.
Find all values of r such that y=erx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.
r= -5,8

milkshake Sep 9, 2014

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Best Answer

$$\\y"-3y'-40y=0.\\\\
Try \\
y=e^{rx}\qquad y'=re^{rx} \qquad y"=r^2e^{rx}\\\\
\mbox{The question becomes}\\\\
r^2e^{rx}-3re^{rx}-40e^{rx}=0\\\\
e^{rx}(r^2-3r-40)=0\\\\
e^{rx}(r-8)(r+5)=0\\\\
\mbox{The only solutions to this are }
r=8\;\; and\;\; r=-5$$

Melody Sep 9, 2014

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Melody · Answer 1 · 2014-09-09T01:37:14

$$\\y"-3y'-40y=0.\\\\
Try \\
y=e^{rx}\qquad y'=re^{rx} \qquad y"=r^2e^{rx}\\\\
\mbox{The question becomes}\\\\
r^2e^{rx}-3re^{rx}-40e^{rx}=0\\\\
e^{rx}(r^2-3r-40)=0\\\\
e^{rx}(r-8)(r+5)=0\\\\
\mbox{The only solutions to this are }
r=8\;\; and\;\; r=-5$$

.

DragonSlayer554 · Answer 2 · 2014-09-09T01:30:24

Hello. What are we going to find to help you?

And great answer in the negative 1 and negative 2 question.

milkshake · Answer 3 · 2014-09-09T01:35:18

i mea a and c are correct but when i simplify the b as (e^rx)*[(r-8)*(r+5)] i gotta do something else i think

Melody · Answer 4 · 2014-09-09T01:39:06

Dragon, this stuff is way over the top of your head. Sorry mate.

Milkshake,

Does that help?

ThAnswerGuy · Answer 5 · 2014-09-09T01:41:44

this is so confusing I can't help and hey guys.

milkshake · Answer 6 · 2014-09-09T01:55:36

i found the solution for my own!)

(e^0)*[(r-8)*(r+5)]

http://i62.tinypic.com/6iu26h.jpg

ThAnswerGuy · Answer 7 · 2014-09-09T01:58:13

so you searched it?

DragonSlayer554 · Answer 8 · 2014-09-09T02:07:25

I could think of it on top on my head...

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DragonSlayer554 · Answer 9 · 2014-09-09T02:49:04

But great answer, though. Keep it up, or lose the grand war of Camelot.

Let y′′−3y′−40y=0

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Let y′′−3y′−40y=0

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