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3 years ago

PLEASE HELP 30 POINTS

Mathematics

1 answer:

Mila [183]3 years ago

7 0

I haven’t really learned this but I think it’s the second one! :)

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

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3 years ago

The mathematical statement 4 C A means:

shtirl [24]

The mathematical statement 4 C A means that 4 is a subset of A. The "C" symbol is generally used in mathematical statements to mean that the former is a subset of the following statement.

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3 years ago

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The fourth and fifth grade classes at James Madison Elementary School are going on a field trip. There are 87 students in fourth

Anna11 [10]

Answer:

about 7

Step-by-step explanation:

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3 years ago

Pls help show work please

Aloiza [94]

Each bracelet is $5, this can be represented as 5b. (Where b is number of bracelets)

Each necklace is $8, this can be represented as 8n. (Where n is number of necklaces)

We know that the total money raised needs to be at least $100, but it can also be more than that.

So we know that 8n+5b will be greater than or equal too 100.

8n+5b ≥ 100

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3 years ago

Will's Pizza can make 12 pizzas in 45 minutes. How many pizzas can they make in 4 hours?

irina1246 [14]

Answer:

64 pizzas

Step-by-step explanation:

4 hours is 240 minutes

12 x (240 / 45) = 64

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