Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(a) What can you say about a solution of the equation $ y{'} = - y^{2} $ just by looking at the differential equation?

(b) Verify that all members of the family $ y = 1/(x + C) $ are solutions of the equation in part (a).

(c) Can you think of a solution of the differential equation $ y^{'} = - y^{2} $ that is not a member of the family in part (b)?

(d) Find a solution of the initial-value problem.

$ y^{'} = - y^2 $ $ y (0) = 0.5 $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(a) (a) since the derivative $y^{\prime}=-y^{2}$ is always negative (or 0 if $y=0$ ), the function $y$ must be decreasing (or equal to 0 ) on any interval on which it is defined.(b) $$=-y^{2}=\mathrm{RHS}$$(c) $y=0$(d) $$C=2, \text { so } y=\frac{1}{x+2}$$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 1

Modeling with Differential Equations

Missouri State University

Oregon State University

Idaho State University

Boston College

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

33:32

04:44

(a) What can you say abou…

05:45

(a) What can you say about…

05:35

14. (a) What you say about…

04:16

(a) What can YOU say bout …

03:42

(a) Show that every member…

04:07

(a) By inspection find a o…

01:56

04:14

$\begin{array}{l}{\text { …

in this question, we have first derivative off. Why equal negative voice square. So if we differentiate both sides, we will have Why Double dash equal. Negative two y want supply. Why dash? So if we replace, why dash with negative or square? So we will get why Dublin dash equal two y porcine So now we have Why does equal negative y or two So the first derivative is negative than the solution off. This differential equation is decreasing, but also we have the second relative equal to wipe our three. So the second drifted have the same sign as the y value. So the graph off the solution is concave up. When the graph is above the X axis and concave down when it's below the X axis, this is the part a in the question 40 importante we have another function which is why equals one over X plus c. If we differentiate both sides, we will get why dash equals negative one over x plus c all square. So we have satisfied the following differential equation, which is why dash equal negative, wide squish import see while zero Why equals zero is also solution to why dash equal negative. Why Square? And it's not a member off the family off the function. Why equal one over X plus C or what? Early in this question, we will substitute X equals zero and why equal 0.5 toe Get the value off. See? So we have 0.5 equals 1/0 plus C, so in this case, C equals to.

View More Answers From This Book

Find Another Textbook

03:25

Between 2006 and 2016 the number of applications for patents, N, grew by abo…

04:33

The Yearly rate of consumption of natural gas of the city of Toronto is 20.L…

03:24

Question 82ptsOn an exam with mean of p = 70, you have score of X = …

02:21

9:13BackAssignment Details STAT-10-06534Tuesday7) A recent s…

02:55

8) The probability that a given tourist goes to the amusement park is 0.47 ,…

04:37

point) A Canadian male has recently had a Prostate Specific Antigen (PSA) te…

05:48

6.58 Normal probabilities For a normal distribution, find the probability th…

03:53

4.7: A manufacturer of processors for communication devices has established …

02:09

Suppose that only 24% of all drivers come to a complete stop at a particular…

00:53

Form polynomial whose zeros and degree are given.Zeros: 3,3, 5; degree: …