Definition of a Differential Equation
OFFICIAL DEFINITION | DIFFERENTIAL EQUATION
An equation containing the derivative(s), either ordinary or partial, of one or more functions and/or dependent variables, in which the derivatives are with respect to one or more dependent variables, is called a differential equation.
An equation containing the derivative(s), either ordinary or partial, of one or more functions and/or dependent variables, in which the derivatives are with respect to one or more dependent variables, is called a differential equation.
STREET DEFINITION | DIFFERENTIAL EQUATION
A differential equation is any equation involving derivatives.
A differential equation is any equation involving derivatives.
QUICK EXAMPLES
\[\frac{dy}{dx} + xy = 3\] \[y'' - y' + y = 1\] \[\frac{d^2x}{dt^2} = a \quad \text{(acceleration)}\] \[F(t,x,x') = m \frac{d^2x}{dt^2} \quad \text{(Newton's second law, } F=ma \text{)}\] \[x^3 \frac{d^3y}{dx^3} + 2x^2 \frac{d^2y}{dx^2} - x \frac{dy}{dx} + y = 12x^2\] \[x y'' = r \sqrt{1 + (y')^2}\] \[\frac{\partial^2 u}{\partial x \partial t} + \sin{(x)} \frac{\partial u}{\partial t} = t^2\] \[\tan{(y)} u_{xx} - \sin{(x)} u_{xy} + y u_{y} = 4\]
\[\frac{dy}{dx} + xy = 3\] \[y'' - y' + y = 1\] \[\frac{d^2x}{dt^2} = a \quad \text{(acceleration)}\] \[F(t,x,x') = m \frac{d^2x}{dt^2} \quad \text{(Newton's second law, } F=ma \text{)}\] \[x^3 \frac{d^3y}{dx^3} + 2x^2 \frac{d^2y}{dx^2} - x \frac{dy}{dx} + y = 12x^2\] \[x y'' = r \sqrt{1 + (y')^2}\] \[\frac{\partial^2 u}{\partial x \partial t} + \sin{(x)} \frac{\partial u}{\partial t} = t^2\] \[\tan{(y)} u_{xx} - \sin{(x)} u_{xy} + y u_{y} = 4\]
