Internal problem ID [7223]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 503.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)+x^5*diff(y(x),x)+6*x^4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{6}}{6}} x +\frac {c_{2} \left (-\left (-x^{6}\right )^{\frac {5}{6}} 6^{\frac {1}{6}}+x^{6} {\mathrm e}^{-\frac {x^{6}}{6}} \left (\Gamma \left (\frac {5}{6}\right )-\Gamma \left (\frac {5}{6}, -\frac {x^{6}}{6}\right )\right )\right )}{x^{5}} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 39
DSolve[y''[x]+x^5*y'[x]+6*x^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-\frac {x^6}{6}} \left (6 c_1 x-c_2 E_{\frac {7}{6}}\left (-\frac {x^6}{6}\right )\right ) \\ \end{align*}