Internal problem ID [7483]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 765.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 63
dsolve((x^2+2)*diff(y(x),x$2)+3*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x \sqrt {2}+\sqrt {2 x^{2}+4}\right )^{\sqrt {2}}}{\sqrt {x^{2}+2}}+\frac {c_{2} \left (x \sqrt {2}+\sqrt {2 x^{2}+4}\right )^{-\sqrt {2}}}{\sqrt {x^{2}+2}} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 80
DSolve[(x^2+2)*y''[x]+3*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 \cos \left (\sqrt {2} \text {ArcCos}\left (\frac {i x}{\sqrt {2}}\right )\right )-\pi c_2 \sin \left (2 \sqrt {2} \csc ^{-1}\left (\frac {2}{\sqrt {2-i \sqrt {2} x}}\right )\right )}{\sqrt [4]{2} \sqrt {\pi } \sqrt {x^2+2}} \\ \end{align*}