59.1.183 problem 185

Internal problem ID [9355]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 185
Date solved : Monday, January 27, 2025 at 06:01:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

dsolve(x^2*diff(y(x),x$2)-x*(7-x^2)*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (\operatorname {Ei}_{1}\left (-\frac {x^{2}}{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}} c_{2} x^{4}+{\mathrm e}^{-\frac {x^{2}}{2}} c_{1} x^{4}+2 c_{2} x^{2}+4 c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 68

DSolve[x^2*D[y[x],{x,2}]-x*(7-x^2)*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{\frac {1}{2} \left (-x^2-5\right )} \left (c_2 x^6 \operatorname {ExpIntegralEi}\left (\frac {x^2}{2}\right )+16 e^5 c_1 x^6-2 c_2 e^{\frac {x^2}{2}} \left (x^2+2\right ) x^2\right ) \]