Internal problem ID [7016]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 285.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+q y^{\prime }-\frac {2 y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+q*diff(y(x),x)=2*y(x)/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (q x -2\right )}{x}+\frac {c_{2} {\mathrm e}^{-q x} \left (q x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 80
DSolve[y''[x]+q*y'[x]==2*y[x]/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {q x^{3/2} e^{-\frac {q x}{2}} \left (2 (i c_2 q x+2 c_1) \sinh \left (\frac {q x}{2}\right )-2 (c_1 q x+2 i c_2) \cosh \left (\frac {q x}{2}\right )\right )}{\sqrt {\pi } (-i q x)^{5/2}} \\ \end{align*}