59.1.147 problem 149

Internal problem ID [9319]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 149
Date solved : Monday, January 27, 2025 at 06:01:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

dsolve(9*x^2*diff(y(x),x$2)-3*x*(7-2*x^2)*diff(y(x),x)+(25+2*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = x^{{5}/{3}} {\mathrm e}^{-\frac {x^{2}}{3}} \left (c_{1} +c_{2} \operatorname {Ei}_{1}\left (-\frac {x^{2}}{3}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 39

DSolve[9*x^2*D[y[x],{x,2}]-3*x*(7-2*x^2)*D[y[x],x]+(25+2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{3}} x^{5/3} \left (c_2 \operatorname {ExpIntegralEi}\left (\frac {x^2}{3}\right )+2 c_1\right ) \]