Here I will give a simple example of numerical solutions to differential equations.

> alias( y=y(t), y0=y(1), yp0=D(y)(1) ): definition of notations

> eqn := t^2*diff(y,[t$2]) + t*diff(y,t) +(t^2-1)*y =0; This gives the equation of n=1Bessel functions.

> initvals := y0=1, yp0 = 0: Initial conditions. You need two of them for a second order ODE.

> F := dsolve( {eqn, initvals}, y, type=numeric ); Solve it!

> F(3);

> Y := t -> rhs( op(2,F(t) ) ); Transform it into a function Y(t).

> plot(Y,1..10); You can see that the plot looks like a Bessel function.

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