Internal problem ID [6812]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 80.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 83
dsolve(diff(y(x),x$2)-3*x*diff(y(x),x)+(5+2*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\erfi \left (\frac {x \sqrt {2}}{2}\right ) \sqrt {\pi }\, \sqrt {2}\, \left (x^{6}-15 x^{4}+45 x^{2}-15\right ) {\mathrm e}^{\frac {x^{2}}{2}}-2 x \,{\mathrm e}^{x^{2}} \left (x^{2}-11\right ) \left (x^{2}-3\right )\right )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \left (x^{6}-15 x^{4}+45 x^{2}-15\right ) \]
✓ Solution by Mathematica
Time used: 0.585 (sec). Leaf size: 78
DSolve[y''[x]-3*x*y'[x]+(5+2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {x^2}{2}} \left (x^6-15 x^4+45 x^2-15\right ) \left (\sqrt {2 \pi } c_2 \text {Erfi}\left (\frac {x}{\sqrt {2}}\right )+1440 c_1\right )-2 c_2 e^{x^2} x \left (x^4-14 x^2+33\right )}{1440} \\ \end{align*}