Internal problem ID [8143]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 668.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {4 y^{\prime \prime }+x y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve(4*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{8}} x \left (x^{2}-12\right )+c_{2} {\mathrm e}^{-\frac {x^{2}}{8}} x \left (x^{2}-12\right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{8}}}{\left (x^{2}-12\right )^{2} x^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 122
DSolve[4*y''[x]+x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\frac {x^2}{8}} \left (\sqrt {2 \pi } c_2 \left (x^2-12\right ) x^2 \text {erfi}\left (\frac {\sqrt {x^2}}{2 \sqrt {2}}\right )+4 \sqrt {x^2} \left (2 \sqrt {2} c_1 x^3-c_2 e^{\frac {x^2}{8}} x^2+8 c_2 e^{\frac {x^2}{8}}-24 \sqrt {2} c_1 x\right )\right )}{32 \sqrt {x^2}} \]