Internal problem ID [8181]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 706.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(x^2*diff(y(x),x$2)+x*(x+1)*diff(y(x),x)+(3*x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \,{\mathrm e}^{-x} \left (x -3\right )+\frac {c_{2} \left (x^{2} {\mathrm e}^{-x} \left (x -3\right ) \operatorname {Ei}_{1}\left (-x \right )+x^{2}-2 x -1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 66
DSolve[x^2*y''[x]+x*(x+1)*y'[x]+(3*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (c_2 (x-3) x^2 \operatorname {ExpIntegralEi}(x)+6 c_1 x^3-x^2 \left (c_2 e^x+18 c_1\right )+2 c_2 e^x x+c_2 e^x\right )}{6 x} \]