Solve a Sturm–Liouville Problem for the Airy Equation
Solve an eigenvalue problem for the Airy equation.
In[1]:=
eqns = {-y''[x] + x y[x] == \[Lambda] y[x], y[0] == 0, y[1] == 0};In[2]:=
sol = DSolveValue[eqns, y[x], x, Assumptions -> 1 < \[Lambda] < 300];List the eigenvalues for the problem.
In[3]:=
eigvals = {ToRules[sol[[1, 1, 2]]]}Out[3]=
Find the eigenfunctions for this problem.
In[4]:=
eigfuns = (sol[[1, 1, 1]] /. {C[1] -> 1})Out[4]=
Plot the eigenfunctions for the range 
.
In[5]:=
Plot[Evaluate[eigfuns /. eigvals], {x, 0, 1}]Out[5]=
