Internal problem ID [9528]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1198.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(x^2*diff(diff(y(x),x),x)-(x^2-2*x)*diff(y(x),x)-(3*x+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-{\mathrm e}^{x} \operatorname {expIntegral}_{1}\left (x \right ) c_{2} x^{3}+{\mathrm e}^{x} x^{3} c_{1} +c_{2} \left (x^{2}-x +2\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 41
DSolve[(-2 - 3*x)*y[x] - (-2*x + x^2)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x x-\frac {c_2 \left (e^x x^3 \operatorname {ExpIntegralEi}(-x)+x^2-x+2\right )}{6 x^2} \]