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3 years ago

Is a proportional function f(x) = 5x linear? Why or why not? Explain with an example. k= 5/1

Mathematics

1 answer:

baherus [9]3 years ago

5 0

Do you still need help with it I can help you?

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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:

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

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

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

(it means your solution is right)

3 0

2 years ago

Solve the equation x-12=2

OverLord2011 [107]

x - 12 = 2

Add 14 to both sides to seperate x from numerical values.

x = 14

6 0

4 years ago

Read 2 more answers

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!

blagie [28]

Answer:

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3 years ago

Customers at the Palace Pro Shop receive a 10% discount if they are members.All customers must pay 7% in sales tax. The function

Dahasolnce [82]

The answer to y’all txt would be 10 buddy

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4 years ago

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Jake bought bought a set of drums that were on sale. The original price of the drums was $300. They were 10% off. How much was t

cestrela7 [59]

Answer:

The sale price before tax was $270

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3 years ago