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djyliett [7]
3 years ago
8

Solve the following differential equation: (1− 5 y +x) dy/dx +y= 5/x −1 . C=

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer:

y(1+x)+x-5\ln xy=C

Step-by-step explanation:

Consider the given differential equation is

(1-\frac{5}{y}+x)\frac{dy}{dx}+y=\frac{5}{x}-1

(1-\frac{5}{y}+x)\frac{dy}{dx}=\frac{5}{x}-1-y

(1-\frac{5}{y}+x)dy=(\frac{5}{x}-1-y)dx

Taking all variables on right sides.

(1-\frac{5}{y}+x)dy-(\frac{5}{x}-1-y)dx=0

(-\frac{5}{x}+1+y)dx+(1-\frac{5}{y}+x)dy=0

Let as assume,

M=-\frac{5}{x}+1+y and N=1-\frac{5}{y}+x

Find partial derivatives \frac{\partial M}{\partial y} and \frac{\partial N}{\partial x}

\frac{\partial M}{\partial y}=1 and \frac{\partial N}{\partial x}=1

Since \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}, therefore the given differential equation is exact.

The solution of the exact differential equation is

\int Mdx+\int N(\text{without x)}dy=C

\int (-\frac{5}{x}+1+y)dx+\int (1-\frac{5}{y})dy=C

yx-5\ln x+x+y-5\ln y=C

y+x+xy-5\ln x-5\ln y=C

y(1+x)+x-5(\ln x+\ln y)=C

y(1+x)+x-5\ln xy=C

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C2+ 10

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5 0
3 years ago
2(3+9x) answer this for me plz lol
Gre4nikov [31]

Answer:

6+18x

Step-by-step explanation:

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4 0
2 years ago
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Please help! I'll give out the brainiest!
gavmur [86]
To find the solution
-4x>36
divide both sides by -4
(REMEMBER WHEN YOU DIVIDE BY A NEGATIVE, THE SIGN FLIPS OVER)
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6 0
3 years ago
ANSWER ASAPPP PLSSS. ILL MARK BRAINLIEST TOO
nevsk [136]

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

3 0
2 years ago
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In august Janet's clothing store sold 234 shirts with the ratio of short sleeves to long sleeves being 9:4. how many short sleev
makvit [3.9K]
162 short sleeve shirts; if you add 9 and 4, you get 13. Then, divide 234 by 13, which equals 18. 18 multiplied by 9 is 162.
3 0
3 years ago
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