#### Question Details

(solution) Please help me with the question 7. Please help me with the

Please help me with the question 7.

Please help me with the question 7.

Please help me with the question 7.

Please help me with the question 7.

Math 331.07 Homework 2: First order ODEs Due Thursday 9/29 Name:

1. Find the order of the following differential equations (y = y(x)). Do NOT solve them:

(a) xy 00 + y = x3

(b) y 0 + y 2 = 2

(c) sin y 000 + 3x2 y = 6x

(d) y 00 (y 0 )1/2 ? 1/y = 0

2. Verify that the function y = y(x) given is a solution of the following ODEs.

(a) y 0 + 4y = 1.4,

(b) y 0 = y + ex , y = e?4x + 0.35

y = (1 + x)ex (c) y 0 tan x = 2y ? 8, y = 4sin2 x + 4 3. Solve the following IVP:

dy

= 4e?t cos t,

dt y(0) = 0 4. Find the general solution to the following Separable ODEs:

(a) y 3 y 0 + x3 = 0

(b) y 0 sin (2?x) = ?y cos (2?x)

5. Solve the following initial value problems (IVPs):

(a) xy 0 = 2 (y ? 4),

0 y(1) = 1 (b) y = 2y (2 ? y), y(0) = 1 (c) y 0 y = 4 sin (2x), y(0) = 1 6. The population of the US was 8.6 Million in 1820 and 40 Million in 1897. Consider

that the rate of change of the population is proportional to the population.

(a) Write down the differential equation for population growth in this case.

(b) Calculate the number of people in the US according to your model in the year

2003. Note that the actual population of the US in 2003 was 291 Million.

7. Boyle-Mariotte?s law for ideal gases (found experimentally by physicists Robert Boyle

and Edme Mariotte) states that for a fixed amount of an ideal gas kept at constant

temperature and low pressure p, the rate of change of the volume V = V (p) equals

?V /p. Solve the model and then explain your outcome. Math 331 Homework Assignment 2 Page 2 of 2 8. Find the general solution to the following first-order linear ODEs. In addition, find

the particular solution whenever an initial condition is provided.

(a) y 0 + y = 1

.

1+ex (b) xy 0 + (x + 1) y = x, with y(ln 2) = 1.

(c) y 0 ? 2y ? x2 e2x = 0, with y(0) = 0.

9. Solve the initial value problem (IVP)

t2 + 4 y 0 + 2ty ? t2 t2 + 4 = 0, y(0) = 3/5.

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Sep 13, 2020 *

* * Solution~00021147720705.docx (25.37 KB)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDSep 13, 2020

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.