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2 years ago

Which one is right ???????

Mathematics

1 answer:

wel2 years ago

3 0

Neither, you just multiply the numerators to get 1, then multiply the denominators to get 6. It is 1/6

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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)

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

6 0

2 years ago

Hanna says you cannot represent the fraction 1/4 on the number line.

blsea [12.9K]

Answer: tHE SECOND ONE

Step-by-step explanation: i had a test on this

5 0

2 years ago

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Help please 50 points

Hatshy [7]

For this, it is kind of like a triangle and having to find the diagonal. Let's see what the two legs of the triangle would be.
Leg one= 7 units
Leg two= 8 units
8²+7²= c²
64 + 49=113
√113≈10.6
The line is 10.6 units long.

4 0

2 years ago

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I really need help on this question!!!

Cloud [144]

Answer: 45 mph

Step-by-step explanation:

We know that Rob was driving 63 mph which is 18 miles faster than pigeons, therefore you subtract to get the answer.

63-18=45

6 0

3 years ago

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