Internal problem ID [9529]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1194.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (-1+3 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(x^2*diff(diff(y(x),x),x)+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: 0.089 (sec). Leaf size: 66
DSolve[(-1 + 3*x)*y[x] + x*(1 + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (c_2 (x-3) x^2 \operatorname {ExpIntegralEi}(x)+6 c_1 x^3-x^2 \left (c_2 e^x+18 c_1\right )+2 c_2 e^x x+c_2 e^x\right )}{6 x} \]