Internal problem ID [8333]
Book: Collection of Kovacic problems
Section: section 3. Problems from Kovacic related papers
Problem number: David Saunders 1981 paper. Example 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (x^{2}+3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)= (x^2+3)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} x +c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \left (\sqrt {\pi }\, \operatorname {erf}\left (x \right ) x +{\mathrm e}^{-x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 46
DSolve[y''[x]== (x^2+3)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x^2}{2}} \left (-\sqrt {\pi } c_2 e^{x^2} x \text {erf}(x)+c_1 e^{x^2} x-c_2\right ) \]