Internal problem ID [7736]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 249.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 58
dsolve(x^2*diff(y(x),x$2)+x*(5-x)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{2}-4 x +2\right )}{x^{2}}+\frac {c_{2} \left (\frac {x^{2} \operatorname {expIntegral}_{1}\left (-x \right )}{4}+\frac {x \,{\mathrm e}^{x}}{4}-\operatorname {expIntegral}_{1}\left (-x \right ) x -\frac {3 \,{\mathrm e}^{x}}{4}+\frac {\operatorname {expIntegral}_{1}\left (-x \right )}{2}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 48
DSolve[x^2*y''[x]+x*(5-x)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \left (x^2-4 x+2\right ) \operatorname {ExpIntegralEi}(x)+4 c_1 \left (x^2-4 x+2\right )-c_2 e^x (x-3)}{4 x^2} \]