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labwork [276]
3 years ago
15

Find a particular solution to y" - y + y = 2 sin(3x)

Mathematics
1 answer:
leonid [27]3 years ago
8 0

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

     =e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}

Multiplying both sides of equation (1) by integrating factor and integrating we get

\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I

I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx

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3 years ago
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Solve the equation 3x + 4 = 5x - 8​
CaHeK987 [17]

Answer:

x = 6

Step-by-step explanation:

3x + 4 = 5x - 8

==> add 8 to both sides

in doing so we get 3x + 4 + 8 = 5x - 8 + 8

the -8 and the +8 cancels out and 4 + 8 = 12

we are left with 3x + 12 = 5x

==> subtract 3x from both sides

in doing so we get 3x - 3x + 12 = 5x - 3x

the 3x and -3x cancel out and 5x - 3x = 2x

we are left with 12 = 2x

==> divide both sides by 2

in doing so we get 12/2 which equals 6 and 2x/2x which leaves us with

6 = x

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2 years ago
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Let f be a twice-differentiable function for all real numbers x. Which of the following additional properties guarantees that f
Mkey [24]

Answer:

(C) f’(c) = 0 and f”(c) > 0

Step-by-step explanation:

A minimum occurs where the first derivative is 0 (the tangent line is horizontal), and the second derivative is positive (concave up).  The simplest example of this is a positive parabola, like y = x², which has a relative minimum at its vertex.

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3 years ago
SOLVE
Ber [7]

Answer:

Step-by-step explanation:

Numer 1:  The answer to this problem is 4 pounds

Numer 2: 13 cups

Explanation:

Four jars of sauce with 26 oz would be a total of 104 ounces

4 x 26 = 104

1 cup contains 8 ounces.

104 oz x \frac{1cps}{8oz}=13 cups

Numer 3: Since,  1 quartz = 33.307 ounces ( approx )

⇒ 3 quartz  = 99.921 ounces

If the total number of players = 16,

And, the given fluid is divided equally among these players,

Then the total quantity of fluid each player get

\frac{toral quality od drink }{ total players}

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=6.24505625= 6.245

Hence, each player will get around 6.245 ounces of the drink.

Number 4:

36 inches or 3 feet is the correct answer

Number 5 ;

The correct answer for the question that is being presented above is this one: "10 pounds." An office supply company is shipping a case of wooden pencils to a store. There are 64 boxes of pencils in the case. If each box of pencils weighs 2.5 ounces, then...

There are:  

64 boxes of pencils

1 box weighs 2.5 ounces

Find its total weight in pounds.

1 ounce = 0.0625 pounds

64 boxes * 2.5 ounces = 160 ounces

160 ounces * 0.0625 pounds/1 oz = 10 pounds.

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3 years ago
6 feet<br> 12 feet<br> What is the area of the given composite shape?
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Answer:

choice A; 128.52 square feet

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This shape is made up of a semi-circle and a rectangle. The area of the rectangle will be 12*6 = 72 sq ft.

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Since pi is infinite we round it to 3.14.

Plug in the values and our expression will be (3.14*6^{2})/2 because it is a semi-circle. Simplify that to (3.14*36)/2 = 113.04/2 = 56.52 sq ft.

Remember to add the area of the rectangle and semi-circle. 72 + 56.52 = 128.52 sq ft.

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2 years ago
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