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Karo-lina-s [1.5K]
3 years ago
5

Solve the boundary value problem

Cfrac%7Bdy%7D%7Bdx%7D%20-%205y%3D0" id="TexFormula1" title=" \frac{d^{2}y}{dx^{2}} + 4 \frac{dy}{dx} - 5y=0" alt=" \frac{d^{2}y}{dx^{2}} + 4 \frac{dy}{dx} - 5y=0" align="absmiddle" class="latex-formula">
y(0)=0
y( \pi /2)=1
Mathematics
1 answer:
Sonja [21]3 years ago
6 0
Characteristic equation:

r^2+4r-5=(r+5)(r-1)=0\implies r=-5,r=1

\implies y_c=C_1e^{-5x}+C_2e^x

Given that y(0)=0 and y\left(\dfrac\pi2\right)=1, you have

\begin{cases}0=C_1+C_2\\1=C_1e^{-5\pi/2}+C_2e^{\pi/2}\end{cases}\implies C_1=\dfrac{e^{5\pi/2}}{1-e^{3\pi}},C_2=-\dfrac{e^{5\pi/2}}{1-e^{3\pi}}

so that the particular solution is

y=\dfrac{e^{5\pi/2}}{1-e^{3\pi}}(e^{-5x}-e^x)
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How many terms would you distribute the factor 4
Mekhanik [1.2K]

Answer:

Factors       Multiples

1, 2, 4    4      16

8 0
3 years ago
The height of a desk is 11 inches shorter than the height of a chair. The height of the chair is 41 inches.
defon

Answer:

equation: y=41-11

answer: the desk is 30 inches.

Step-by-step explanation:

So if the desk is 11 inches SHORTER than the chair, and the height of the chair is 41 inches, all you need to do is subtract 11 from 41, which will give you a total of 30 inches.

Hope this helps!

8 0
3 years ago
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Write 5.9/100 as a percent
leonid [27]
Here is your answer:

<span>5.9/100 * 100 = 0.059
0.059 * 100 = 5.9%
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Therefore the answer is "5.9%."

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5 0
4 years ago
Solve the equation (0°≤A≤360°)<br>a) √3sinA-cosA=√2​
Blizzard [7]

Step-by-step explanation:

√3sinA-cosA=√2

dividing both side by (√3²-1²=2 we get)

√3/2 sinA-1/2.cos A=√2/2

cos 30sinA-sin30cosA=√2/(√2×√2)

sinAcos30-cosAsin30=1/√2

sin(A-30)=sin45,sin(180-45)

therefore

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6 0
3 years ago
The length of a garden box is 6 feet longer than 4times the width. If the length of the garden box is 22 feet, what is the width
erica [24]

Answer:

Width of the garden box = 4 feet

Step-by-step explanation:

Given that:

Length of garden box = 22 feet

Let,

w be the width of garden box

It is also given that:

The length of a garden box is 6 feet longer than 4 times the width.

L = 4w + 6

Putting L = 22

22 = 4w + 6

22 - 6 = 4w

4w = 16

Dividing both sides by 4

\frac{4w}{4}=\frac{16}{4}\\w=4

Hence,

Width of the garden box = 4 feet

7 0
3 years ago
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