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# What is nonlinear ordinary differential equation?

Updated: 9/28/2022

Wiki User

14y ago

An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt².

In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation.

A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example

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