Internal problem ID [6799]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 67.
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^{6} y^{\prime }+7 x^{5} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)+x^6*diff(y(x),x)+7*x^5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{7}}{7}} x +c_{2} \left ({\mathrm e}^{-\frac {x^{7}}{7}} 7^{\frac {6}{7}} \left (-x^{7}\right )^{\frac {1}{7}} \Gamma \left (\frac {6}{7}\right )-{\mathrm e}^{-\frac {x^{7}}{7}} 7^{\frac {6}{7}} \left (-x^{7}\right )^{\frac {1}{7}} \Gamma \left (\frac {6}{7}, -\frac {x^{7}}{7}\right )+7\right ) \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 39
DSolve[y''[x]+x^6*y'[x]+7*x^5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{7} e^{-\frac {x^7}{7}} \left (7 c_1 x-c_2 E_{\frac {8}{7}}\left (-\frac {x^7}{7}\right )\right ) \\ \end{align*}