Internal problem ID [7413]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 694.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.138 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-9/4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{i x} \left (x +i\right )}{x^{\frac {3}{2}}}+\frac {c_{2} {\mathrm e}^{-i x} \left (-x +i\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 44
DSolve[x^2*y''[x]+x*y'[x]+(x^2-9/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {2}{\pi }} ((c_1 x+c_2) \cos (x)+(c_2 x-c_1) \sin (x))}{x^{3/2}} \\ \end{align*}