Internal problem ID [8328]
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]]
\[ \boxed {y^{\prime \prime }-\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 67
dsolve(diff(y(x),x$2)= (1/4*x^2-1/2-5)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{4}} x \left (x^{4}-10 x^{2}+15\right )+c_{2} {\mathrm e}^{-\frac {x^{2}}{4}} x \left (x^{4}-10 x^{2}+15\right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{2}}}{\left (x^{4}-10 x^{2}+15\right )^{2} x^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 22
DSolve[y''[x]== (1/4*x^2-1/2-5)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}(-6,i x)+c_1 \operatorname {ParabolicCylinderD}(5,x) \]