Internal problem ID [6798]
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]]
\[ \boxed {y^{\prime \prime }+x^{6} y^{\prime }+7 y x^{5}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)+x^6*diff(y(x),x)+7*x^5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x^{7}}{7}} x +\frac {c_{2} \left (-\left (-x^{7}\right )^{\frac {6}{7}} 7^{\frac {1}{7}}+x^{7} {\mathrm e}^{-\frac {x^{7}}{7}} \left (\Gamma \left (\frac {6}{7}\right )-\Gamma \left (\frac {6}{7}, -\frac {x^{7}}{7}\right )\right )\right )}{x^{6}} \]
✓ Solution by Mathematica
Time used: 0.093 (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 \operatorname {ExpIntegralE}\left (\frac {8}{7},-\frac {x^7}{7}\right )\right ) \\ \end{align*}