For questions about ordinary differential equations, which are differential equations involving ordinary derivatives of one or more dependent variables with respect to a single independent variables. For questions specifically concerning partial differential equations, use the [tag:pde] instead.

A differential equation is any expression that relates the values of a collection of functions and their derivatives, as well as some coefficients. One may be asked to solve (symbolically or numerically) or estimate the solution to a differential equation. Usually, they appear as the result of a mathematical model for a physical phenomenon.

The $n^{th}$ order ordinary differential equation is of the form $$F[x, y, \frac{dy}{dx}, \frac{d^2y}{dx^2}, . . . ,\frac{d^n y}{dx^n}]=0$$ where $F$ is real function of its $n+2$ arguments $x, y, \frac{dy}{dx}, \frac{d^2y}{dx^2}, . . . ,\frac{d^n y}{dx^n}$.


Some times we use the prime notation for derivatives as $$F(x, y, y', y'', . . . , y^{(n)})=0$$ where the notations $y'\equiv\frac{dy}{dx}, y''\equiv\frac{d^2y}{dx^2}$ and so on.

References:

"Differential Equations" by Shepley L. Ross

"Differential Equations With Applications and Historical Notes" by G.F. Simmons

https://en.wikipedia.org/wiki/Ordinary_differential_equation

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This tag is intended for ordinary differential equations, i.e., the differential equations which contain only derivatives w.r.t. one variable and not partial derivatives.

Use the tag for partial differential equation questions.