Solving Differential Equations: Step-by-Step Guide for Homework

In summary, the conversation discusses finding the solution to a first order, linear ODE with the equation dv/dx + 1/200 = 32/v. The individual asking for assistance is unsure of how to begin and is advised to identify the type of ODE and use the appropriate method. It is determined that the ODE is separable and the suggested method is to write the ODE in the form dv/dx = f(v). The individual is grateful for the help provided.
  • #1
sara_87
763
0

Homework Statement



i want to find the solution to:
dv/dx + 1/200 = 32/v

Homework Equations





The Attempt at a Solution



I don't know how to begin. what would be my first step?
 
Physics news on Phys.org
  • #2
Can you identify which type of ODE it is? I.e. homogeneous/inhomogeneous, linear/non-linear etc.
 
  • #3
first order, linear
isn't it?
 
  • #4
sara_87 said:
first order, linear
isn't it?
It is indeed, so which method does one usually use for solving first order, linear ODE's?
 
  • #5
do multiply everything by v? or can we use the coefficient of v^(-1) to find the integrating factor?
 
  • #6
sara_87 said:
do multiply everything by v?
I would multiply it be v first, which puts the ODE into canonical form, and then find the IF.
 
  • #7
are we allowed to have v*(dv/dx)?
because when i did i got:

[ve^(x/200)]dv/dx + (v/200)e^(x/200) = 32e^(x/200)

i don't think that's right
 
  • #8
Ohh dear, was I am thinking?! The ODE is separable, try writing the ODE in the form,

[tex]\frac{dv}{dx}=f(v)[/tex]

Sorry about that, I had a stupid moment :uhh:
 
  • #9
its ok i always have stupid moments.
Thank you very much u've been much help.
 

1. What are differential equations?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They involve variables, functions, and their respective rates of change.

2. How are differential equations used in science?

Differential equations are used in a variety of scientific fields, such as physics, engineering, and biology, to model and predict the behavior of systems and processes. They are also used to analyze and solve complex problems in these fields.

3. What is the difference between ordinary and partial differential equations?

Ordinary differential equations involve a single independent variable, while partial differential equations involve multiple independent variables. Ordinary differential equations also have a single solution, while partial differential equations have a family of solutions.

4. Can differential equations be solved analytically?

Some simple differential equations can be solved analytically, but most require numerical methods or approximations to find a solution. The complexity of the equation and the initial conditions also play a role in determining if an analytical solution is possible.

5. How are differential equations solved numerically?

Numerical methods, such as Euler's method or the Runge-Kutta method, are used to approximate the solution to a differential equation. These methods involve breaking the equation into smaller steps and using iterative calculations to find an approximate solution.

Similar threads

  • Calculus and Beyond Homework Help
Replies
10
Views
409
  • Calculus and Beyond Homework Help
Replies
7
Views
132
  • Calculus and Beyond Homework Help
Replies
14
Views
235
  • Calculus and Beyond Homework Help
Replies
7
Views
640
  • Calculus and Beyond Homework Help
Replies
2
Views
669
Replies
7
Views
465
  • Calculus and Beyond Homework Help
Replies
2
Views
533
  • Calculus and Beyond Homework Help
Replies
5
Views
846
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
624
Back
Top