59.3.3 problem Kovacic 1985 paper. page 15. Weber equation

Internal problem ID [10005]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Kovacic 1985 paper. page 15. Weber equation
Date solved : Monday, January 27, 2025 at 06:16:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)= (1/4*x^2-1/2-5)*y(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{4}} \left (15 \operatorname {hypergeom}\left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right ) c_{2} +x c_{1} \left (x^{4}-10 x^{2}+15\right )\right )}{15} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]== (1/4*x^2-1/2-5)*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}(-6,i x)+c_1 \operatorname {ParabolicCylinderD}(5,x) \]