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3 years ago

I’m like super confused can somebody help me please?

Mathematics

1 answer:

Nezavi [6.7K]3 years ago

4 0

Equations are steeper when their slope's positive value is higher (ignore negatives when determining how steep a slope is). The slope is the value in front of x. If there isn't a value in front of x, then it is assumed to be 1.

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Solve this problem by using variation of parameters method.<br> y''-y=coshx.

Gekata [30.6K]

$y''-y=0\implies r^2-1=0\implies r=\pm1$
$\implies y_c=C_1e^x+C_2e^{-x}={C^*}_1\underbrace{\cosh x}_{y_1}+{C^*}_2\underbrace{\sinh x}_{y_2}$

For the nonhomogeneous ODE

$y''-y=\underbrace{\cosh x}_{f(x)}$

we're looking for a particular solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\int\frac{y_2(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the two fundamental solutions.

We have

$W(y_1,y_2)=\begin{vmatrix}\cosh x&\sinh x\\\sinh x&\cosh x\end{vmatrix}=\cosh^2x-\sinh^2x=1$

so we're left with

$u_1=-\displaystyle\int\sinh x\cosh x\,\mathrm dx=-\dfrac12\cosh^2x$
$u_2=\displaystyle\int\cosh^2x\,\mathrm dx=\dfrac12x+\dfrac14\sinh2x$

so that the particular solution is

$y_p=-\dfrac12\cosh^3x+\dfrac12x\sinh x+\dfrac14\sinh x\sinh2x$
$y_p=-\dfrac12\cosh x+\dfrac12x\sinh x$

As $y_1$ already accounts for the $\cosh x$ term in $y_p$ , we're left with the general solution

$y=C_1\cosh x+C_2\sinh x+\dfrac12x\sinh x$

3 0

3 years ago

Jejehrhehekjejrbehjehrbebe

poizon [28]

Answer:

What??????????????

5 0

3 years ago

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The ratio of people who wanted hot dogs to hamburgers was 5:8. If 52 meals were served how many of those were hot dogs and hambu

nata0808 [166]

Answer:

32 hamburgers, 20 hot dogs

Step-by-step explanation: 5+8=13. then you divide 52 by 13 that equals 4 and then multiply the hot dog 5 times 4 = 20 and 8 times 4= 32

5 0

2 years ago

You invest $3,000 in an account that has an annual interest rate of 2.5%, compounded continuously. How much money will be in the

denis-greek [22]

Here' s the equation for one year:
0.025(3000) + 3000
Because it is 5 years:
5(0.025(3000)) + 3000
0.075(3000) + 3000
We can make it simpler:
1.075(3000)
Multiply:
3225
You will have $3225

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3 years ago

Which pairs of triangles MUST be similar?

Anon25 [30]

Answer:

B. 3&4 are isosceles.

Step-by-step explanation:

Not 100% sure, just kind of makes sense

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3 years ago

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