Internal problem ID [8147]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 672.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(3*x^2*diff(y(x),x$2)-x*(x+8)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {2}{3}} {\mathrm e}^{\frac {x}{3}} \left (x^{2}-2 x +4\right )+c_{2} x^{\frac {2}{3}} {\mathrm e}^{\frac {x}{3}} \left (x^{2}-2 x +4\right ) \left (\int \frac {x^{\frac {4}{3}} {\mathrm e}^{-\frac {x}{3}}}{\left (x^{2}-2 x +4\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 79
DSolve[3*x^2*y''[x]-x*(x+8)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{x/3} x^{2/3} \left (x^2-2 x+4\right )-\frac {c_2 e^{x/3} x^{2/3} \left (x^2-2 x+4\right ) \Gamma \left (\frac {1}{3},\frac {x}{3}\right )}{6\ 3^{2/3}}+\frac {1}{6} c_2 (x-4) x \]