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LekaFEV [45]
3 years ago
5

Please show me how to solve the initial value problem y'=tanx y(pi/4)=3

Mathematics
1 answer:
AlexFokin [52]3 years ago
4 0
The ODE is separable, i.e. you can write

\dfrac{\mathrm dy}{\mathrm dx}=\tan x\iff\mathrm dy=\tan x\,\mathrm dx

Integrating both sides gives the general solution.

\displaystyle\int\mathrm dy=\int\tan x\,\mathrm dx
y=-\ln|\cos x|+C

Given that y\left(\dfrac\pi4\right)=3, we have

3=-\ln\left|\cos\dfrac\pi4\right|+C
3=-\ln\dfrac1{\sqrt2}+C
3-\ln\sqrt2=C


and so the particular solution to the IVP is

y=-\ln|\cos x|+3-\ln\sqrt2
y=3-\ln|\sqrt2\cos x|
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Y= (x-9) (x+3)
juin [17]

Answer:

y = x² − 6x − 27

Step-by-step explanation:

To distribute, you can use something called FOIL.  It stands for First, Outer, Inner, Last.

First, multiply the First term in each factor.

x · x = x²

Now multiply the Outer terms in each factor.

x · 3 = 3x

Next multiply the Inner terms in each factor.

-9 · x = -9x

Finally, multiply the Last terms in each factor.

-9 · 3 = -27

Add them all up:

x² + 3x − 9x − 27

x² − 6x − 27

4 0
3 years ago
What divided by 8 to equal 3
blsea [12.9K]

Answer:

Nothing

Step-by-step explanation:

You can't divide 8 to equal 3 because 3 is an odd number and 8 is an even number.

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5 0
2 years ago
What is 2x-5/3=7?<br><br> Plz help!
ki77a [65]
Hello! And thank you for your question!

First add 5/3 to both sides:

2x = 7 + 5/3

Then simplify 7 + 5/3:

2x = 26/3

Then divide both sides by 2:

x = 26/3 over 2

After that simplify 26/3/2:

x = 26 over 3 x 2

Simplify 3 x 2:

x = 26/6

Simplify:

x = 13/3 or 4 1/3

Final Answer:

x = 13/3 or 4 1/3
5 0
3 years ago
Help me <br>Help me <br>Please​
Leno4ka [110]

Answer:

y = 1/2x + -3

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Divide 2x2 +5x+2 by 2x+1​
Serggg [28]

the answer is   [    x + 2   ]

8 0
2 years ago
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