1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Will give brainliest-This graph compares shoe sizes for a group of 80 two-year-old boys and a group of 60 three-year-old boys. A
IgorLugansk [536]
To answer this question you need to know that the box and whisker plot take the data set and represent it fourths. Each section (half of the box or each whisker is 25% of the data.

So, for the 2 year old boys, half of them or 50% of the shoe sizes were 6 or less (40) and for the 3 year olds it was 1/4 or 25% of them (1/4 x 60= 15).

40-15= 25 more two year olds have a shoes size of 6 or less.
6 0
3 years ago
Read 2 more answers
What is 1(4x+7y)+2(5y-9x)​
patriot [66]
1(4x+7y)+2(5y-9x)
=4x+7y+10y-18x
=-14x+17y

The solution is -14x+17y.
3 0
3 years ago
After his alarm rings, Clarence has
Sonja [21]

Answer: 14 days

Step-by-step explanation:

Day 1: 1 minute snooze = 24 minutes

Day 2: 2 minute nooze = 23 minutes ; these examples show snooze time = days.

We can set up an equation for this situation: 25 - s = r ; where s = snooze time and r = time to get ready.

Given the problem, we can fill out this equation with: 25 - s = 11

When you solve this equation, time snoozed = 14.

We already know that snooze time = days, so days = 14.

I am not a professional, simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

7 0
3 years ago
3 T-shirts cost $12. How<br> much will 50 T-shirts<br> cost?
LekaFEV [45]

Answer:

$200

Step-by-step explanation:

First, find the unit rate:

12/3= 4

Then multiply:

4*50= 200

Hope this helps!

6 0
2 years ago
Read 2 more answers
Given the endpoint A(1, 3) and the midpoint C(6, 2), find the other endpoint B(x, y).
Tpy6a [65]

Right away we know we don't have fractions; the midpoint is the average of the coordinates, so if it and one endpoint are integers so is the other endpoint.

We can do a kind of point arithmetic:

C = (A+B)/2

2C = A+B

B = 2C - A

B = 2(6,1) - (1,3) = (12,2)-(1,3)=(11,-1)

Answer: That's none of the above, but a typo away from the first choice.

6 0
3 years ago
Other questions:
  • 3/8 + 5/-6 in simplest form<br><br> 3/8 + 5/-6 in simplest form
    14·1 answer
  • Geometry help , only answer if your sure please. The question is in the attached
    15·1 answer
  • What is true about the solution to the system of inequalities shown?
    9·1 answer
  • Please help (15 points!!!!) asap
    6·1 answer
  • Samantha bought a calculator.she gave the cashier$50 and received$2 in change. How many did the calculator cost?
    14·2 answers
  • Please help me idk this
    11·2 answers
  • 2
    12·1 answer
  • Please please please help me I’ll give brainly
    7·1 answer
  • Select the correct location on the coordinate plane.
    9·1 answer
  • Use the graph below to solve the system of equations? {y = x - 2 {y= -2x + 7
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!