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2 years ago

8

One third of the sum of a number and four

1 answer:

STatiana [176]2 years ago

4 0

Answer:

$\frac{1}{3} (n+4)$

That is what the expression would be

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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

X^2+4x-5/1-x how do you simplify it?

Elodia [21]

<span><span><span>x^2</span></span><span><span>+<span>4x</span></span><span>-5</span></span></span> using the AC method.<span><span><span>(<span>x<span>−1</span></span>)</span><span>(<span>x+5</span>)/</span></span><span>1<span>−<span>x
which gives you -x-5</span></span></span></span>

7 0

3 years ago

Read 2 more answers

Identify a solution to this system of equations -4x+3y=23, x-y=-7

Komok [63]

bearing in mind that a solution to a system of equations is where their graph intersect or meets, Check the picture below.

6 0

3 years ago

Determine the value of x and y in the following systems of equations5x-2y=4 ; -2x+y=2.

V125BC [204]

Answer:(x,y)=(8,18)

Step-by-step explanation:

Given

5x-2y=4-------1

Second Equation

-2x+y=2-----2

Now multiply equation 2 by 2 and it to equation 1

5x-4x+0=8

x=8

substitute it in equation 1

$5\times 8-2\times y=4$

36=2y

y=18

Therefore

(x,y)=(8,18)

7 0

3 years ago

How many triangles can be constructed with angles measuring 120°, 40°, and 10°?

balu736 [363]

Any kind of Triangle must have 180 degree of angle in total if it is not, then it is not a Triangle.

In short, Your Answer would be Zero

Hope this helps!

6 0

3 years ago

Read 2 more answers