Why doesn't this work? What do you understand by v-substitution?Schmoozer said:I tried v-substitution and just couldn't get a v to fit.
Perhaps better to rewrite it asSchmoozer said:Homework Statement
"Solve the following ODE's:"
"3u+(u+x)u'=0"
This is our first weeks homework and he went this through this so quickly in class.
Homework Equations
None. x and u are both variables.
The Attempt at a Solution
I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?
Thanks guys!
A first order, non linear, homogeneous ODE (ordinary differential equation) is a mathematical equation that describes the relationship between a function and its derivatives. It is a first order equation because it only involves the first derivative of the function. It is non linear because it contains non-linear terms, meaning that the function and its derivatives are raised to powers or multiplied together. It is homogeneous because all of the terms in the equation have the same degree.
2.The main difference between linear and non linear ODEs is the form of the equation. In a linear ODE, the function and its derivatives are only multiplied by constants, while in a non linear ODE, they may be raised to powers or multiplied together. This means that the solutions to linear ODEs can often be found using algebraic methods, while non linear ODEs often require more advanced techniques such as numerical methods or series solutions.
3.Solving a first order, non linear, homogeneous ODE involves finding a function that satisfies the equation. This can be done using various techniques such as separation of variables, substitution, or integrating factors. The specific method used will depend on the form of the equation and the techniques that the solver is comfortable with. In some cases, it may not be possible to find an exact solution and numerical methods may be used instead.
4.ODEs are used in many different fields of science and engineering to model a wide range of phenomena. Non linear, homogeneous ODEs, in particular, are often used to describe systems that exhibit non-linear behavior, such as chemical reactions, population dynamics, and electrical circuits. They are also used in economics, biology, and physics to model complex systems.
5.While first order, non linear, homogeneous ODEs can model many real-world systems, they do have some limitations. In some cases, the equations may be too simplified to accurately describe the behavior of the system. Additionally, finding an exact solution to a non linear ODE can be difficult or even impossible, which may require the use of numerical methods. Furthermore, ODEs only provide a mathematical description of a system and may not take into account other factors and variables that can affect the system in the real world.