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katen-ka-za [31]

3 years ago

6

18x^2-2 factor completely

1 answer:

vladimir1956 [14]3 years ago

5 0

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Consider the differential equation x^2 y''-xy'-3y=0. If y1=x3 is one solution use redution of order formula to find a second lin

Anastasy [175]

Suppose $y_2(x)=y_1(x)v(x)$ is another solution. Then

$\begin{cases}y_2=vx^3\\{y_2}'=v'x^3+3vx^2//{y_2}''=v''x^3+6v'x^2+6vx\end{cases}$

Substituting these derivatives into the ODE gives

$x^2(v''x^3+6v'x^2+6vx)-x(v'x^3+3vx^2)-3vx^3=0$

$x^5v''+5x^4v'=0$

Let $u(x)=v'(x)$ , so that

$\begin{cases}u=v'\\u'=v''\end{cases}$

Then the ODE becomes

$x^5u'+5x^4u=0$

and we can condense the left hand side as a derivative of a product,

$\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C$

$x^5u=C\implies u=Cx^{-5}$

Solve for $v$ :

$v'=Cx^{-5}\implies v=-\dfrac{C_1}4x^{-4}+C_2$

Solve for $y_2$ :

$\dfrac{y_2}{x^3}=-\dfrac{C_1}4x^{-4}+C_2\implies y_2=C_2x^3-\dfrac{C_1}{4x}$

So another linearly independent solution is $y_2=\dfrac1x$ .

3 0

3 years ago

A city held a bike parade. 52 bikers rode in the parade, and 8 of them rode a fixed-gear bicycle.

Vedmedyk [2.9K]

Answer:

$\frac{2}{13}$

Step-by-step explanation:

Find the probability by dividing the number of fixed gear bikers by the total number of bikers in the parade.

Since there are 8 fixed gear bikers and 52 bikers in total, this will be found by dividing 8 by 52.

So, the probability as a fraction is $\frac{8}{52}$

This can be simplified by dividing both the numerator and denominator by 4:

= $\frac{2}{13}$

So, the probability is $\frac{2}{13}$

6 0

3 years ago

Dalton's sister Dorina plays basketball and makes 84% of her free throws. If she attempts 225 free

mrs_skeptik [129]

She would make C. 189

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2 years ago

Westbury Jeep paid $10,000 for a boat at auction. At the dealership, a salesperson sold the boat for

pogonyaev

Answer:

C.

Step-by-step explanation:

5 0

3 years ago

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What is the length of the leg in a right triangle whose hypotenuse is 13 and other leg is 12.

Talja [164]

It is 5 because you have to do 12 squared minus 13 squared and then square root that which equals 5

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3 years ago

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