Exercises 10.7(a) and 10'.7(a)

?NDSolve

We use NDSolve to find the numerical solution:

solution = 
      NDSolve[{y''[x] == -100*x*y[x], y[0] == 1, 
          y[1] == 2}, y[x], {x, 0, 1}]

Now, lets look at the value of the solution at various points:

u[x_] := Evaluate[y[x] /. solution]

u[1/2]

u[1/4]

Here's the initial slope u' at t=0:

u'[0]

Lets plot the solution:

Plot[u[x], {x, 0, 1}]