Internal problem ID [7501]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((x^2+6*x)*diff(y(x),x$2)+(3*x+9)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +3\right )+\frac {c_{2} \left (2 x^{2}+12 x +9\right )}{\sqrt {x^{2}+6 x}} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 82
DSolve[(x^2+6*x)*y''[x]+(3*x+9)*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {9 \sqrt {\pi } c_2 \sqrt [4]{-x (x+6)} Q_{\frac {3}{2}}^{\frac {1}{2}}\left (\frac {x}{3}+1\right )+\sqrt {6} c_1 \left (2 x^2+12 x+9\right )}{9 \sqrt {\pi } \sqrt [4]{-x^2} \sqrt {x+6}} \]