Internal problem ID [7572]
Book: Collection of Kovacic problems
Section: section 3. Problems from Kovacic related papers
Problem number: Kovacic 1985 paper. page 15. Weber equation.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)= (1/4*x^2-1/2-5)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{4}} \hypergeom \left (\left [-2\right ], \left [\frac {3}{2}\right ], \frac {x^{2}}{2}\right ) x +c_{2} {\mathrm e}^{-\frac {x^{2}}{4}} \hypergeom \left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[y''[x]== (1/4*x^2-1/2-5)*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 D_{-6}(i x)+c_1 D_5(x) \\ \end{align*}