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
MatroZZZ [7]
2 years ago
7

Solve the initial value problems: 1/θ(dy/dθ) = ysinθ/(y^2 + 1); subject to y(pi) = 1

Mathematics
1 answer:
ladessa [460]2 years ago
5 0

Answer:

-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi  - \frac{1}{2}

Step-by-step explanation:

Given the initial value problem \frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\ subject to y(π) = 1. To solve this we will use the variable separable method.

Step 1: Separate the variables;

\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\frac{1}{\theta}(\frac{dy}{sin\theta d\theta} ) =\frac{ y}{y^{2}+1 } \\\frac{1}{\theta}(\frac{1}{sin\theta d\theta} ) = \frac{ y}{dy(y^{2}+1 )} \\\\\theta sin\theta d\theta = \frac{ (y^{2}+1)dy}{y} \\integrating\ both \ sides\\\int\limits \theta sin\theta d\theta =\int\limits  \frac{ (y^{2}+1)dy}{y} \\-\theta cos\theta - \int\limits (-cos\theta)d\theta = \int\limits ydy + \int\limits \frac{dy}{y}

-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y +C\\Given \ the\ condition\ y(\pi ) = 1\\-\pi cos\pi +sin\pi  = \frac{1^{2} }{2} + ln 1 +C\\\\\pi + 0 = \frac{1}{2}+ C \\C = \pi  - \frac{1}{2}

The solution to the initial value problem will be;

-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi  - \frac{1}{2}

You might be interested in
Solve the quadratic equation by graphing: (2 – 7) + 2 = 38 CHOOSE ALL THAT APPLY
RoseWind [281]

The solution is the x-value of the point of intersection.

x ≈ 1 ,1 3

6 0
3 years ago
Predict the number of sales in month 5? help ASAP please
balandron [24]
It is dividing by 2 each time so the number of sales is 545.
8 0
3 years ago
Choose the correct correspondence RT​
Marizza181 [45]

<u></u>RT corresponds to TR. correct option b.

<u>Step-by-step explanation:</u>

In the given parallelogram or rectangle , we have a diagonal RT . We need to find which side is in correspondence with side/Diagonal RT of parallelogram URST .

<u>Side TU:</u>

In triangle UTR , we see that TR is hypotenuse and is the longest side among UR & TU . So , TR can never be equal in length to UR & TU . So there's no correspondence of Side TU with RT.

<u>Side TR:</u>

Since, direction of sides are not mentioned here , we can say that TR & RT is parallel & equal to each other . So , TR is in correspondence with side/Diagonal RT of parallelogram URST .

<u>Side UR:</u>

In triangle UTR , we see that TR is hypotenuse and is the longest side among UR & TU . So , TR can never be equal in length to UR & TU . So there's no correspondence of Side UR with RT.

4 0
3 years ago
3. About how much of the earth's surface is deserts?
Murrr4er [49]

Answer:

B- One-Quarter

Step-by-step explanation:

8 0
2 years ago
I’ll give a brainiest to the correct answer!!!!
Kay [80]
Answer: 7
Explanation: both triangles are congruent, so the mid segment is half of 14
5 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone help on this?
    9·2 answers
  • John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere o
    11·1 answer
  • Line D passes through the points (1, 1) and (5, 6). What is the slope of a line perpendicular to Line D?
    5·1 answer
  • find the volume of a right circular cone that has a height of 2.1m and a base with a diameter of 13.7m. round your answer to the
    13·1 answer
  • N/3 ≤ 3<br><br> Solve the Inequality and show all work!
    14·2 answers
  • PLEASE HELP, WILL GIVE BRAINLIEST FOR RIGHT ANSWER!
    14·2 answers
  • The length of a shadow of a tree is 74 feet. If the angle of elevation from the end of the shadow to the
    6·1 answer
  • Solve the equation for the indicated variable. <br> P = 2L + 2W for L
    12·1 answer
  • Question down below! ty if u help&lt;3
    7·2 answers
  • DO NOT GIVE AN ANSWER FOR ME TO DOWNLOAD...<br> 3x+8 &lt; 14 JUST GIVE THE ANSWER PLS
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!