Internal problem ID [8154]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 679.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (-3+x \right ) y^{\prime }+\left (-x +4\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)+x*(x-3)*diff(y(x),x)+(4-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} x^{2}+c_{2} x^{2} {\mathrm e}^{-x} \operatorname {expIntegral}_{1}\left (-x \right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 22
DSolve[x^2*y''[x]+x*(x-3)*y'[x]+(4-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} x^2 (c_2 \operatorname {ExpIntegralEi}(x)+c_1) \]