How to covert this differential equation into a system of one order ODE?

Thread starter nufeng
Start date Nov 6, 2012
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Differential Differential equation Ode System

In summary, a differential equation is a mathematical equation used to describe the behavior of a system over time. Converting it into a system of one order ODE allows for easier solving and a better understanding of the system's behavior. This is done by identifying variables and their derivatives and creating a system of equations. While there are benefits to this method, it may not be applicable to all differential equations and can result in a more complex system to solve. It is important to consider the specific problem before using this approach.

Nov 6, 2012

nufeng

How to covert this differential equation into a system of one order ODE?
x^2*y''-2*x*y'+2*y = 0;
y(1) = 4; y'(1)=0;
solve for y(x)

I tried to convert it
get

X' = AX
in which
X = [y, z]'
A = [0, 1; 2/x^2, 2/x];

But x exists in A, which cannot solve by dsolve in Matlab.

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Nov 7, 2012

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Related to How to covert this differential equation into a system of one order ODE?

1. What is a differential equation?

A differential equation is a mathematical equation that relates the rate of change of a variable to the value of the variable itself. It is used to describe the behavior of a system over time.

2. Why do we need to convert a differential equation into a system of one order ODE?

Converting a differential equation into a system of one order ODE allows us to break down a complex equation into smaller, simpler equations that are easier to solve. It also helps us to understand the behavior of the system in a more detailed manner.

3. How do we convert a differential equation into a system of one order ODE?

To convert a differential equation into a system of one order ODE, we need to first identify the variables and their derivatives in the equation. Then, we can create a system of equations by setting each derivative equal to a new variable and writing the original equation in terms of these new variables.

4. What are the benefits of converting a differential equation into a system of one order ODE?

Converting a differential equation into a system of one order ODE allows us to better understand the behavior of the system and make predictions about its future behavior. It also makes solving the equation more manageable and can lead to more accurate solutions.

5. Are there any limitations to converting a differential equation into a system of one order ODE?

Yes, there are some limitations to converting a differential equation into a system of one order ODE. This method may not be applicable to all types of differential equations, and it may also result in a more complex system of equations to solve. It is important to consider the specific problem and determine if this method is the most appropriate approach.