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2 years ago

SOMEONE PLEASE HELP ME CLICK ON THE PDF AND SCROLL DOWN AND ANSWER 7-12

Mathematics

1 answer:

algol132 years ago

5 0

Answer:

Is there a way u can show a picture instead of us having to download it?

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Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu

Alisiya [41]

Let $y=C_1x+C_2x^3=C_1y_1+C_2y_2$ . Then $y_1$ and $y_2$ are two fundamental, linearly independent solution that satisfy

$f(x,y_1,{y_1}',{y_1}'')=0$
$f(x,y_2,{y_2}',{y_2}'')=0$

Note that ${y_1}'=1$ , so that $x{y_1}'-y_1=0$ . Adding $y''$ doesn't change this, since ${y_1}''=0$ .

So if we suppose

$f(x,y,y',y'')=y''+xy'-y=0$

then substituting $y=y_2$ would give

$6x+x(3x^2)-x^3=6x+2x^3\neq0$

To make sure everything cancels out, multiply the second degree term by $-\dfrac{x^2}3$ , so that

$f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y$

Then if $y=y_1+y_2$ , we get

$-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0$

as desired. So one possible ODE would be

$-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0$

(See "Euler-Cauchy equation" for more info)

6 0

2 years ago

The price of tickets for the dance was 1 ticket for $6 or 2 tickets for $8 she looked inside the cash box and found $200 and tic

Aleks04 [339]

We can say that exchanging one couple's ticket for an individual's ticket would increase the money in the cash box from 200 to 202 and it would result in an even number of couples tickets sold.

Step-by-step explanation:

Let the number of tickets sold to the individuals = s

Let the number of tickets sold to the couples = c

According to the question,

s + c = 46 ( Equation 1)

Since each individual's ticket is $6, the total amount of money made by selling tickets to individuals is 6s.

Similarly, since each ticket sold to couples is $8, the total amount of money made by selling tickets to couples is 8c.

So,

6 s + 8 c = 200 ( Equation 2)

On solving both the equations, we get

c = 38 and s = 8

Therefore, 8 tickets were sold to individuals and 38 tickets were sold to the couples.

5 0

2 years ago

What is Use the table to solve the inequality 2x<2. x −1 0 1 2 3 2x

Vedmedyk [2.9K]

Answer:

x less than 1

Step-by-step explanation:

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2 years ago

10 to the zero power times 2 to the 1 power

bezimeni [28]

the answer is two :D

8 0

1 year ago

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umka2103 [35]

For what shape??
pls answer, then we can get somewhere with this question!! :)

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2 years ago

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