Bernouilli ODE (where is my mistake?)

Thread starter justaboy
Start date Sep 24, 2010
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Mistake Ode

In summary, Bernouilli ODE is a type of differential equation used to model physical phenomena where the rate of change of a variable is proportional to a power of the variable itself. The main difference between Bernouilli ODE and other types of ODEs is the appearance of the dependent variable in both the function and its derivative with a different power. It has various real-life applications in fields such as physics and economics. When solving Bernouilli ODE, common mistakes include forgetting to divide by the power of the dependent variable and not applying initial conditions correctly. To check if a solution is correct, one can plug it back into the original equation and graph it for comparison.

Sep 24, 2010

justaboy

found my mistake... thanks

Last edited: Sep 24, 2010

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Sep 24, 2010

jackmell

justaboy said:

Homework Statement

Solve the ODE
[tex]x^2y'+2xy-y^3=0[/tex]

The Attempt at a Solution

[tex]x^2y'+2xy-y^3=0[/tex]
Substitution:
[tex]v=y^-2[/tex]
V makes the equation linear:
[tex]v'-4\frac{v}{x}=-2x^{-2}[/tex]

I get:

[tex]v'+\frac{4}{x} v=-\frac{2}{x^2}[/tex]

FAQ: Bernouilli ODE (where is my mistake?)

1. What is Bernouilli ODE?

Bernouilli ODE (Ordinary Differential Equation) is a type of differential equation that is used to model certain physical phenomena in which the rate of change of a variable is proportional to a power of the variable itself.

2. What is the difference between Bernouilli ODE and other types of ODEs?

The main difference between Bernouilli ODE and other types of ODEs is that the dependent variable appears both in the function and in its derivative with a different power.

3. What are some real-life applications of Bernouilli ODE?

Bernouilli ODE is commonly used in physics to model phenomena such as population growth, chemical reactions, and fluid flow. It is also used in economics to model supply and demand dynamics.

4. What are some common mistakes made when solving Bernouilli ODE?

One common mistake is forgetting to divide by the power of the dependent variable when isolating it on one side of the equation. Another mistake is not applying the initial conditions correctly, which can lead to incorrect solutions.

5. How can I check if my solution to a Bernouilli ODE is correct?

You can check your solution by plugging it back into the original equation and seeing if it satisfies the equation. You can also graph your solution and compare it to the graph of the original equation to see if they match.