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3 years ago

Help please!!!

Mathematics

1 answer:

Keith_Richards [23]3 years ago

8 0

Answer:

x=-34/3 or x=-11.333333333333 or x=-11 1/3

Step-by-step explanation:

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1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

The fraction subtracted from 5/3 to get 1 is_____

siniylev [52]

Answer:

2/3

Step-by-step explanation:

I am not sure

7 0

2 years ago

Read 2 more answers

a store makes a profit of 25$ on each graphing calculator it sells. how many calculators must the store sell to make a profit of

Irina18 [472]

11 because 275÷25 is 11. 11 calculators would cost 275 in total

4 0

2 years ago

Please help quick lol

sergiy2304 [10]

Hello!!

here's ur answer...

given that the volume of cube=343cm³

side³=343cm³

side=³√343

side=7cm

verification:-

volume of cube=side³

=7×7×7

=343cm³

hence, verified.

the length of the edge of cube is 7cm.

hope this helps....

8 0

3 years ago

Your car invoice reads: “Price $1,492.50, dealer preparation $45.00, transportation $54.50, undercoat $148.80, 60-day guarantee

Maurinko [17]

Answer:$2,074.53

Step-by-step explanation:

Final cost will be calculated as the sum of each expense stated on the invoice, which is $1,492.50 + $45 + $54.50+ $148.80 + $95 + $238.73 = $2,074.53

Final cost = $2,074.53, i hope this helps, please mark as brainliest answer.

7 0

2 years ago