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kkurt [141]
2 years ago
11

9) work out 6 - 3x-2--10​

Mathematics
1 answer:
Kaylis [27]2 years ago
3 0
3x+6 I believe because you can’t add a number with a variable to a number without 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}

6 0
3 years ago
What can you conclude about the tangent lines and the diameter of a circle?
svetlana [45]

Answer:

B. perpendicular Hope this helps!

6 0
2 years ago
A pizza shop charged $49.57 for 3 large pepperoni pizzas. This price included a $2.50 delivery fee.
Simora [160]
15.69 because 49.57-2.50 divided by 3 =15.69
7 0
3 years ago
Read 2 more answers
in a random School sampling of 50 middle school students it was found that 18 students bring their lunch to school everyday if t
dem82 [27]

Answer:

340

Step-by-step explanation:

We can see in the sample that 18/50 people bring lunches to school. If we divide 18 by 50 we get 0.36 now we know that 36% of people bring their lunches in the sample. Now we take that number and multiply it by 942.

0.36*942= 339.12 which we can round to 340

5 0
2 years ago
Mrs Richmond bought some apples and pears in the ratio 2:5. An apple costs 30 cents. A pear costs 15 cents mire than an apple. H
Lera25 [3.4K]

Answer:

$2.85

Step-by-step explanation:

30×2=60

30+15=45

60+(45×5)=?

45×5=225

60+225=285

$2.85

Cuz every 100cents is one dollar

5 0
3 years ago
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