Ordinary Differential Equations

Solve a linear ordinary differential equation:

y'' + y = 0

w"(x)+w'(x)+w(x)=0

Specify initial values:

y'' + y = 0, y(0)=2, y'(0)=1

Solve an inhomogeneous equation:

y''(t) + y(t) = sin t

x^2 y''' - 2 y' = x

Solve an equation involving a parameter:

y'(t) = a t y(t)

Solve a nonlinear equation:

f'(t) = f(t)^2 + 1

y"(z) + sin(y(z)) = 0

Find differential equations satisfied by a given function:

differential equations sin 2x

differential equations J_2(x)

Numerical Differential Equation Solving

Solve an ODE using a specified numerical method:

Runge-Kutta method, dy/dx = -2xy, y(0) = 2, from 1 to 3, h = .25

{y'(x) = -2 y, y(0)=1} from 0 to 2 by implicit midpoint

Specify an adaptive method:

solve {y'(x) = -2 y, y(0)=1} from 0 to 10 using r k f algorithm