- #1

strohm

- 1

- 0

y(0) = 0

I tried separating the variables, but it doesn't work.

Thanks in advance.

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In summary, A first order non-linear ODE is a mathematical equation describing the relationship between a function and its derivatives, involving non-linear terms. To solve it, one must separate the variables, transform the equation, and integrate both sides. Non-linearity in ODEs can lead to complex behavior and there are numerical methods to solve them. These equations can be used to model real-world phenomena.

- #1

strohm

- 1

- 0

y(0) = 0

I tried separating the variables, but it doesn't work.

Thanks in advance.

Physics news on Phys.org

- #2

nonequilibrium

- 1,439

- 2

A first order non-linear ODE (ordinary differential equation) is a mathematical equation that describes the relationship between a function and its derivatives. Unlike linear ODEs, non-linear ODEs involve non-linear terms, meaning that the dependent variable is raised to a power or multiplied by itself.

The general approach to solving a first order non-linear ODE is to separate the dependent and independent variables, transform the equation into a separable form, and then integrate both sides. This will result in a solution that includes an arbitrary constant, which can be determined by applying initial or boundary conditions.

Non-linearity in ODEs can arise in many physical systems and can lead to more complex behavior compared to linear systems. Non-linear ODEs can exhibit chaotic behavior, multiple solutions, and sensitivity to initial conditions, making them challenging to solve and understand.

Yes, there are several numerical methods for solving non-linear ODEs, such as Euler's method, Runge-Kutta methods, and the shooting method. These methods involve approximating the solution at discrete points and can be used to solve non-linear ODEs that do not have analytical solutions.

Yes, non-linear ODEs are commonly used to model a wide range of physical phenomena, including population growth, chemical reactions, and electrical circuits. These models may require more complex equations and techniques to solve, but they can provide a more accurate representation of real-world systems.

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