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ryzh [129]
3 years ago
6

Find the general solution to 3y′′+12y=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants

and x the independent variable. Enter c1 as c1 and c2 as c2.
Mathematics
1 answer:
lozanna [386]3 years ago
4 0

Answer:

y(x)=c_1e^{2ix}+c_2e^{-2ix}

Step-by-step explanation:

You have the following differential equation:

3y''+12y=0     (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i

The solution of the differential equation is:

y(x)=c_1e^{m_1x}+c_2e^{m_2x}   (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

y(x)=c_1e^{2ix}+c_2e^{-2ix}

You might be interested in
Which number in the set {6, 12, 18, 36} satisfies the equation below? 6x - 18 = 54
svp [43]

Answer:

12

Step-by-step explanation:

Solving the equation would be the easiest way to find out which number fits.

6x - 18 = 54

6x = 72

x = 12

4 0
2 years ago
Write the standard form of the equation of the line through the given point with the given slope. Through (-2,5), slope =-4
AleksandrR [38]

Answer:

\huge\boxed{4x+y=-3}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

<em>(x₁, y₁)</em><em> - point on a line</em>

<em>m</em><em> - slope</em>

<em />

We have

m=-4,\ (-2,\ 5)\to x_1=-2,\ y_1=5

Substitute:

y-5=-4(x-(-2))\\\\y-5=-4(x+2)

Convert to the standard form

Ax+By=C

y-5=-4(x+2)                <em> use the distributive property</em>

y-5=(-4)(x)+(-4)(2)

y-5=-4x-8               <em>add 5 to both sides</em>

y-5+5=-4x-8+5

y=-4x-3               <em>add 4x to both sides</em>

4x+y=-4x+4x-3\\\\4x+y=-3

3 0
3 years ago
Please help with both problems
erica [24]
Okay so i cant figure out the first one, but the second one looks like -7:3
8 0
2 years ago
PLEASE HELP ME ASAP!! Write the following statement as an inequality: 8 less than a number w is under 35.
Lesechka [4]

Answer:

8<w<35

Step-by-step explanation:

the w has to be over 8, but less than 35, so 8<w<35 is ur answer.

// have a great day //

3 0
3 years ago
Tap on photo<br><br> Answer ASAP!<br><br> Extra points!!!
sukhopar [10]

Answer:

84mm²

Step-by-step explanation:

A=Formula for area of a triangle: \frac{1}{2\\}(B×H)

A=  \frac{1}{2\\}(14×12)

A=  \frac{1}{2\\}(168)

A= 84mm²

3 0
3 years ago
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