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Musya8 [376]
3 years ago
6

Solve the differential equation. y' + 5xey = 0.

Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer:

The solution is     y = - ln(\frac{5}{2}x^{2} + C)

Step-by-step explanation:

To solve the differential equation, we will find y

From the given equation, y' + 5xey = 0.

That is, y' + 5xe^{y} = 0

This can be written as

\frac{dy}{dx} + 5xe^{y} = 0

Then,

\frac{dy}{dx} = - 5xe^{y}

\frac{dy}{e^{y}}   = - 5x dx

Then, we integrate both sides

\int {\frac{dy}{e^{y}}}  =\int {- 5x dx}

\int {e^{-y}dy }}  =\int {- 5x dx}

Then,

-e^{-y} = -\frac{5}{2}x^{2} + C

e^{-y} = \frac{5}{2}x^{2} + C

Then,

ln(e^{-y}) = ln(\frac{5}{2}x^{2} + C)

Then,

-y = ln(\frac{5}{2}x^{2} + C)

Hence,

y = - ln(\frac{5}{2}x^{2} + C)

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Answer:

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Zander = Z

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Z=15 3/4(5/6)

Z=13 1/8

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Hope this helps!

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3 years ago
What is 30x pulse 80x
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Read 2 more answers
Write the standard form equation of the ellipse shown in the graph, and identify the foci.
vlada-n [284]

Answer option A

From the given graph is a Vertical ellipse

Center of ellipse = (-2,-3)

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The distance between center and vertices = 6, so a= 6

The distance between center and covertices = 4 , so b= 4

The general equation of vertical ellipse is

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(h,k) is the center

we know center is (-2,-3)

h= -2, k = -3 , a= 6  and b = 4

The standard equation  becomes

\frac{(x+2)^2}{4^2} + \frac{(y+3)^2}{6^2}=1

\frac{(x+2)^2}{16} + \frac{(y+3)^2}{36}=1

Foci  are (h,k+c)  and (h,k-c)

c=\sqrt{a^2-b^2}

Plug in the a=6  and b=4

c=\sqrt{6^2-4^2}

 c=\sqrt{20}

  c=2\sqrt{5}, we know h=-2  and k=-3

Foci  are   (-2,-3+2\sqrt{5})  and  (-2,-3-2\sqrt{5})

Option A is correct

6 0
3 years ago
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frosja888 [35]
Your answer is B. 12. 

12 kids are unaccounted for after you subtract the kids that take A1, then A2, the both subjects. 
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