Internal problem ID [6960]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 229.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+x y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 42
dsolve(4*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{8}} \hypergeom \left (\left [-1\right ], \left [\frac {3}{2}\right ], \frac {x^{2}}{8}\right ) x +c_{2} {\mathrm e}^{-\frac {x^{2}}{8}} \hypergeom \left (\left [-\frac {3}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 64
DSolve[4*y''[x]+x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{32} \left (\sqrt {2} e^{-\frac {x^2}{8}} x \left (x^2-12\right ) \left (\sqrt {\pi } c_2 \text {Erfi}\left (\frac {x}{2 \sqrt {2}}\right )+8 c_1\right )-4 c_2 \left (x^2-8\right )\right ) \\ \end{align*}