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2 years ago

I NEEDDD HELP PLEASE!!! this is due today!

Mathematics

1 answer:

ozzi2 years ago

8 0

Answer:

What is it love ?

Step-by-step explanation:

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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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2 years ago

Which order from least to greatest of 2.8, 2.8x10², 2.8x10⁻3, 2.8x10⁴, 2.8x10⁻5

Dominik [7]

2.8x10^-5 ; 2.8x10^-3 ; 2.8 ; 2.8x10^2 ; 2.8x10^4

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MATH<br><br> HELP<br><br> FIND THE EQUATION OF THE LINE

Dominik [7]

y=3/3x+-2

Step-by-step explanation:

it goes up 3 and over 3 so its 3/3 and it starts at -2

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topjm [15]

Answer:

3cos(3t)

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What do you think the answer is, please hurry

vazorg [7]

There is an 18% chance that out of the 3 students she asks, 3 would be in a band. I hope this helped ^^

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