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aliya0001 [1]
3 years ago
10

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

tions. make sure that your equation is free of the arbitrary parameters c1 and c2.
Mathematics
1 answer:
Alisiya [41]3 years ago
6 0
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)
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Your friends and you notice a classmate who always has brand new clothes, shoes, and electronics. What would you need to know in
sashaice [31]

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

<h3>What is an asset?</h3>

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

Learn more about assets on:

brainly.com/question/25746199

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5 0
2 years ago
Nate borrowed $62,000 at 9.4% interest per year if he owed a total of $910.90 in when he repaid the loan how many days do they k
OverLord2011 [107]
The formula for simple annual interest is:

I = Prt

where,

I = Interest accumulated = $910.90
P = Principal Amount = $62000
r = Interest rate = 9.4% = 0.094
t = time in years

Using the values in above equation, we get:

910.90 = 62000 x 0.094 x t

⇒ t = 910.90/(62000 x 0.094) = 0.156

This is the time in years. Since there are 365 days in a year, the time in days will be:

t = 0.156 x 365 = 57 (rounded to nearest day)

This means, Nate kept the borrowed money for 57 days
6 0
3 years ago
A large pizza has 16 slices. You eat 4 pieces and 7 chicken wings. What proportion of the pizza did you eat?
ddd [48]

Answer:

4/16

Step-by-step explanation:

You ate 4 slice of the 16 slice pizza

3 0
3 years ago
Simplify expression x8y-26/x14y-5 × x-39y-21
koban [17]

The simplified form of the expression is x^{-45} y^{-42}

<h3>Simplifying an expression</h3>

From the question, we are to simplify the given expression

The given expression is

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

The expression can be simplified as shown below

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

\frac{x^{8} \times x^{-39} \times  y^{-26} \times  y^{-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8+-39} \times  y^{-26+-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8-39} \times  y^{-26-21}  }{x^{14} \times y^{-5}  }

\frac{x^{-31} \times  y^{-47}  }{x^{14} \times y^{-5}  }

Then,

\frac{x^{-31} }{x^{14} } \times \frac{ y^{-47} }{ y^{-5} }

x^{-31-14} \times y^{-47--5}

x^{-31-14} \times y^{-47+5}

x^{-45} \times y^{-42}

x^{-45} y^{-42}

Hence, the simplified form of the expression is x^{-45} y^{-42}

Learn more on Simplifying an expression here: brainly.com/question/2320607

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3 0
2 years ago
5a +4b+c-3a-c+4b simplified
MAVERICK [17]

Answer:

2a + 8b

Step-by-step explanation:

4 0
3 years ago
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