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dangina [55]
3 years ago
7

Brainlies please give me one 100 pontes if you give me a brainlies (give me a brainlies)

Mathematics
2 answers:
Crazy boy [7]3 years ago
3 0

Answer:

ok i will

Step-by-step explanation:

none

Leviafan [203]3 years ago
3 0

Answer:

i hope

Step-by-step explanation:

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~Hello! Hope your day or night is good!~

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Step-by-step explanation:

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Solve the linear differential equation 2xy' + y = 2√x
77julia77 [94]

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}

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tresset_1 [31]

Answer:

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Step-by-step explanation:

4/6 + 1/2

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