59.1.812 problem 835

Internal problem ID [9984]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 835
Date solved : Monday, January 27, 2025 at 06:16:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-(x^2+5/4)*y(x) = 0,y(x), singsol=all)
 

\[ y = \frac {\left (x +1\right ) c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x} \left (x -1\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 53

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]-(x^2+5/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {\frac {2}{\pi }} ((i c_2 x+c_1) \sinh (x)-(c_1 x+i c_2) \cosh (x))}{\sqrt {-i x}} \]