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lakkis [162]
3 years ago
6

How do you do this question?

Mathematics
1 answer:
ElenaW [278]3 years ago
6 0

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

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3 0
3 years ago
3(x + y + h)=<br> Can someone help me with this
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4 0
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Rewrite as a quotient of two base - 9 logarithms. write your answer in simplest form log 17 =<br>​
4vir4ik [10]

Answer:

\frac{log_{9}17 }{log_{9}10 }

Step-by-step explanation:

Using the change of base rule for logarithms

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Given

log 17 , that is log_{10} 17 , then

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8 0
3 years ago
Solve for x.
statuscvo [17]

Answer:

The Answer is: x = 1.444 with repeating 4.

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212x - 68x - 170 = 38

212x - 68x = 38 + 170

144x = 208

x = 208/144 = 52/35 or 1.444

Proof:

212(1.444) - 34(2(1.444) + 5) = 38

306.128 - 34(7.888) = 38

306.128 -  268.192 = 37.936 or approximately 38

Hope this helps! Have an Awesome Day!!  :-)

7 0
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:Sarah and bryan went shopping and spent a total of 47:50. bryan spent 15.50 less than what sarah spent. How much did bryan spen
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Answer:

its 32.00

Step-by-step explanation:

47.50

-15.50

---------

32.00

8 0
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