All categories

2 years ago

Pls help immediately!!!!

Mathematics

1 answer:

alexgriva [62]2 years ago

4 0

The correct answer should be A

You might be interested in

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

2 years ago

To calculate 587 ÷ 1,000, how many decimal points to the left should the decimal in 587 move?

VARVARA [1.3K]

Answer:

3 decimal points

Step-by-step explanation:

The trick here is to count the zeros.

8 0

2 years ago

Which expression has a value of 26 when a=4 and b=5

alekssr [168]

Answer:

a=4

Step-by-step explanation:

5 0

2 years ago

What is the output value of 2x^2-9x-5 input value is x=2

Kobotan [32]

Answer:

-15

Step-by-step explanation:

Go to (Mâthway) This page can help you with problems like that. (replace the â with a when searching the site.)

5 0

2 years ago

Which statement is true?

Nata [24]

P(hemoglobin level between 9 and 11) = P(age between 25 and 35 years)..

8 0

3 years ago