Need Help Solving These ODE Problems?

  • Thread starter prison-rat
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In summary, the conversation is about someone asking for help with a few questions and another person offering guidance and solving some of the questions. The first person provides images with the questions and the second person provides solutions with explanations. They discuss topics such as integrals, exact differentials, and characteristic equations. The second person advises the first person to start with question 1 and helps them solve questions 1-2. They also provide helpful tips for solving the remaining questions.
  • #1
prison-rat
2
0
Hi. I have some important questions to solve until tomorrow night..

Can anyone solve them please ?

05.JPG



01
http://img356.imageshack.us/img356/4218/01hz1.jpg

02
http://img356.imageshack.us/img356/4851/02yn6.jpg

03
http://img356.imageshack.us/img356/5762/03pm9.jpg

04
http://img204.imageshack.us/img204/7753/04gr4.jpg



Thank you
 
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  • #2
Welcome to PF!

Hi prison-rat! Welcome to PF! :smile:

Show us what you've done and where you're stuck, and then we'll know how to help you! :wink:

Start with question 1. :smile:
 
  • #3
thanks for your reply.

I solved 1-2 but ımnot sure the re true.
3-4 I am trying
here first 2

http://img514.imageshack.us/img514/3762/answer1rt7.jpg
thanks
 
Last edited by a moderator:
  • #4
You are fine until 2b
[tex]\int \frac{dy}{1- 2y}\ne ln(1- 2y)+ C[/tex]
Let u= 1- 2y and substitute.
 
  • #5
Numbers 3 and 4 look fairly standard. Do you know what an "exact differential" is?

For number 4, notice that there are no odd powers in the characteristic equation.
 

FAQ: Need Help Solving These ODE Problems?

What is an ODE?

An ODE, or ordinary differential equation, is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many natural and physical phenomena, such as the motion of objects, growth of populations, and chemical reactions.

What are some examples of ODEs?

Some common examples of ODEs include the logistic equation, which describes population growth, and the harmonic oscillator equation, which describes the motion of a simple pendulum. Other examples include the heat equation, wave equation, and Navier-Stokes equations, which are used in physics and engineering.

How are ODEs solved?

There are several methods for solving ODEs, including analytical methods such as separation of variables and using special functions, as well as numerical methods like Euler's method and the Runge-Kutta method. The method used depends on the complexity of the ODE and the desired level of accuracy.

What is the difference between an ODE and a PDE?

An ODE is an equation that contains only one independent variable, while a PDE, or partial differential equation, contains multiple independent variables. This means that a PDE involves derivatives with respect to more than one variable, making it more complex to solve.

How are ODEs used in real-world applications?

ODEs are used in many fields, including physics, chemistry, biology, and engineering, to model and understand various phenomena. They can be used to predict the behavior of systems, design control systems, and solve optimization problems. Some specific examples of applications include modeling population growth, predicting the spread of diseases, and designing aircraft control systems.

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