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Degger [83]
3 years ago
11

Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx

= cos(x + y), y(0) = π 2
Mathematics
1 answer:
shutvik [7]3 years ago
5 0

\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)

Let v=x+y, so that \dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}:

\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1

Now the ODE is separable, and we have

\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx

Integrating both sides gives

\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx

For the integral on the left, rewrite the integrand as

\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v

Then

\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C

and so

\csc v-\cot v=x+C

\csc(x+y)-\cot(x+y)=x+C

Given that y(0)=\dfrac\pi2, we find

\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1

so that the particular solution to this IVP is

\csc(x+y)-\cot(x+y)=x+1

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X/3 = 6/9
x= 6/9 x 3/1
x = 18/9 = 2

ANSWER=2
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Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn’s
laiz [17]

Answer:

A

Step-by-step explanation:

|((experimental - theoretical) / theoretical)| x 100

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|-.0213| = .0213

.0213 x 100 = 2.13


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Jorge bought x tickets to attend a football game and a baseball game. The expression 8x + 62 represents the total cost of the fo
rusak2 [61]

Answer:

21

Step-by-step explanation:

Let x be the amount of ticket for each game

Given

The expression 8x + 62 represents the total cost of the football game

The total coat for the.game will be

8(7)+62

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If 9x + 34 represents the total cost of the baseball game. The total coat will be;

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Prove that if a is a natural number, then there exist two unequal natural numbers k and l for which ak−al is divisible by 10.
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Assume a is not divisible by 10. (otherwise the problem is trivial). 
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
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8 0
3 years ago
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