Internal problem ID [7977]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 501.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x^{6}+7 y x^{5}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
dsolve(diff(y(x),x$2)+x^6*diff(y(x),x)+7*x^5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x^{7}}{7}} x +\frac {7 c_{2} \left (-1\right )^{\frac {6}{7}} {\mathrm e}^{-\frac {x^{7}}{7}} \left (-\Gamma \left (\frac {6}{7}\right ) x^{7}+\left (-x^{7}\right )^{\frac {6}{7}} 7^{\frac {1}{7}} {\mathrm e}^{\frac {x^{7}}{7}}+\Gamma \left (\frac {6}{7}, -\frac {x^{7}}{7}\right ) x^{7}\right )}{\left (-x^{7}\right )^{\frac {6}{7}}} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 53
DSolve[y''[x]+x^6*y'[x]+7*x^5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{49} e^{-\frac {x^7}{7}} \left (49 c_1 x-7^{6/7} c_2 \sqrt [7]{-x^7} \Gamma \left (-\frac {1}{7},-\frac {x^7}{7}\right )\right ) \]