Internal problem ID [7235]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 515.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(2*diff(y(x),x$2)+5*x*diff(y(x),x)+(4+2*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x^{2}} c_{1}+c_{2} {\mathrm e}^{-x^{2}} \erf \left (\frac {i \sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 42
DSolve[2*y''[x]+5*x*y'[x]+(4+2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x^2} \left (\sqrt {3 \pi } c_2 \operatorname {Erfi}\left (\frac {\sqrt {3} x}{2}\right )+3 c_1\right ) \\ \end{align*}