Examples for
Differential Equations
A differential equation is an equation involving a function and its derivatives. It can be referred to as an ordinary differential equation (ODE) or a partial differential equation (PDE) depending on whether or not partial derivatives are involved. Wolfram|Alpha can solve many problems under this important branch of mathematics, including solving ODEs, finding an ODE a function satisfies and solving an ODE using a slew of numerical methods.
Ordinary Differential Equations
Solve an ODE or find an ODE a function satisfies.
Solve a linear ordinary differential equation:
y'' + y = 0w"(x)+w'(x)+w(x)=0Specify initial values:
y'' + y = 0, y(0)=2, y'(0)=1Solve an inhomogeneous equation:
y''(t) + y(t) = sin tx^2 y''' - 2 y' = xSolve an equation involving a parameter:
y'(t) = a t y(t)Solve a nonlinear equation:
f'(t) = f(t)^2 + 1y"(z) + sin(y(z)) = 0Find differential equations satisfied by a given function:
differential equations sin 2xdifferential equations J_2(x)Numerically solve a differential equation using a variety of classical methods.