Differential Equations
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)
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
plot a Bessel function
plot J2(x)
integrate a spherical Bessel function
integrate spherical Bessel j3(x)
Spheroidal Functions
evaluate S1 numerically