Internal problem ID [7807]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 321.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve((x^2+2)*diff(y(x),x$2)+3*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (\sqrt {2}\, x +\sqrt {2}\, \sqrt {x^{2}+2}\right )^{\sqrt {2}}}{\sqrt {x^{2}+2}}+\frac {c_{2} {\left (\frac {\sqrt {2}}{2 \sqrt {x^{2}+2}+2 x}\right )}^{\sqrt {2}}}{\sqrt {x^{2}+2}} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 92
DSolve[(x^2+2)*y''[x]+3*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2^{3/4} c_1 \cos \left (2 \sqrt {2} \arcsin \left (\frac {1}{2} \sqrt {2-i \sqrt {2} x}\right )\right )}{\sqrt {\pi } \sqrt {x^2+2}}+\frac {c_2 Q_{-\frac {1}{2}+\sqrt {2}}^{\frac {1}{2}}\left (\frac {i x}{\sqrt {2}}\right )}{\sqrt [4]{x^2+2}} \]