3 years ago

Help brainliest for correct answer

Mathematics

1 answer:

Ksju [112]3 years ago

5 0

Answer:

nooooooooo

Step-by-step explanation:

mark me brainlist

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Let y′′′−9y′′+20y′=0. find all values of r such that y=erx satisfies the differential equation. if there is more than one correc

DerKrebs [107]

we are given

differential equation as

$y'''-9y''+20y'=0$

we are given

$y=e^{rx}$

Firstly, we will find y' , y'' and y'''

those are first , second and third derivative

First derivative is

$y'=re^{rx}$

Second derivative is

$y''=r*re^{rx}$

$y''=r^2e^{rx}$

Third derivative is

$y'''=r^2*re^{rx}$

$y'''=r^3e^{rx}$

now, we can plug these values into differential equation

and we get

$r^3 e^{rx}-9r^2 e^{rx}+20re^{rx}=0$

now, we can factor out common terms

$e^{rx}(r^3 -9r^2 +20r)=0$

we can move that term on right side

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now, we can factor out

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now, we can set them equal

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$r-4=0$

$r=4$

so, we will get

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