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Lina20 [59]
4 years ago
12

Write 10 : 2 in form n : 1

Mathematics
2 answers:
docker41 [41]4 years ago
8 0
N = 5

5 : 1
divide 10 and 2 by 2 :)
netineya [11]4 years ago
4 0
1/2 of 2 is 1
1/2 of 10 is 5...

5:1
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Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

\frac{dy}{dx}+P(x)y=Q(x)

For this case, we can rewrite the equation as:

\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}

Here P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}

To find the solution (y(x)), we can use the integration factor method:

Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx

Then F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}

So, we can find:

y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C

Suppose that x\in \double R, then \sqrt{|x|}=\sqrt{x} , and we find:

y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}

To check our solution is right or not, put your y(x) back to the ODE:

y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}

2xy'=\frac{x-C}{\sqrt{x}}

2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}

(it means your solution is right)

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