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3 years ago

Crystal randomly selects a card from the list and

Mathematics

1 answer:

MariettaO [177]3 years ago

3 0

Sorry, don’t know the answer

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: Show that the solution of the differential equation: = − − − − − is of the form: + + ( − ) = + , When = and =

Serhud [2]

Answer:

$y = \tan(x + \frac{x^2}{2})$

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that $y=\tan(x+\frac{x\²}{2})$

When

$\frac{dy}{dx} =1+xy\²+x+y\²$ and $y(0)=0$

We have:

$\frac{dy}{dx} =1+xy\²+x+y\²$

Rewrite as:

$\frac{dy}{dx} =1+x+xy\²+y\²$

Factorize

$\frac{dy}{dx} = (1+x)+y\²(x+1)$

Rewrite as:

$\frac{dy}{dx} = (1+x)+y\²(1+x)$

Factor out 1 + x

$\frac{dy}{dx} = (1+y\²)(1+x)$

Multiply both sides by $\frac{dx}{1 + y^2}$

$\frac{dy}{1+y\²} = (1+x)dx$

Integrate both sides

$\int \frac{dy}{1+y\²} = \int (1+x)dx$

Rewrite as:

$\int \frac{1}{1+y\²} dy = \int (1+x)dx$

Integrate the left-hand side

$\int \frac{1}{1+y\²} dy = \tan^{-1}y$

Integrate the right-hand side

$\tan^{-1}y = x + \frac{x^2}{2} + c$

$y(0)=0$ implies that: $(x,y) = (0,0)$

So:

$\tan^{-1}y = x + \frac{x^2}{2} + c$ becomes

$\tan^{-1}(0) = 0 + \frac{0^2}{2} + c$

This gives:

$0 = 0 +0 + c$

$0 =c$

$c = 0$

The equation $\tan^{-1}y = x + \frac{x^2}{2} + c$ becomes

$\tan^{-1}y = x + \frac{x^2}{2} + 0$

$\tan^{-1}y = x + \frac{x^2}{2}$

Take tan of both sides

$y = \tan(x + \frac{x^2}{2})$ --- Proved

8 0

3 years ago

I need help for this question. can someone help me

AlexFokin [52]

Answer:

the missing angle is 130

Step-by-step explanation:

180-50=130

5 0

3 years ago

Read 2 more answers

Eorge pays one-fifth of his salary in taxes. If his taxes amount to $217, what is his salary?

Amiraneli [1.4K]

$1,085. Just multiply by 5

5 0

3 years ago

Which graph represents the function f(x)=4⋅3x?

ch4aika [34]

the right answer is first one

8 0

3 years ago

Araine borrows $400 on a 4-year loan. She is charged 5% simple interest per year. How much interest is she charged for 4 years?

DiKsa [7]

Answer:

Interest Charged = $80

Total payback = $480

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Present Value (PV) = $400

Time period (n) = 4 years

Interest rate (r) = 5%

So, we can calculate the future value(FV), by using following formula,

FV = PV ( 1 + n × r)

By putting the value, we get

FV = $400 ( 1 + 4 × 0.05)

= $480

Hence total amount she has to pay back = $480.

Interest charged = FV - PV

= $480 - $400

=$80

5 0

3 years ago