Internal problem ID [6739]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime }+x y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 57
dsolve(3*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left ({\mathrm e}^{-\frac {x^{2}}{6}} \sqrt {6}\, \left (x^{2}+15\right ) x +\left (x^{4}+18 x^{2}+27\right ) \erf \left (\frac {\sqrt {6}\, x}{6}\right ) \sqrt {\pi }\right )+c_{2} \left (x^{4}+18 x^{2}+27\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 43
DSolve[3*y''[x]+x*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{6}} \text {HermiteH}\left (-5,\frac {x}{\sqrt {6}}\right )+\frac {1}{27} c_2 \left (x^4+18 x^2+27\right ) \\ \end{align*}