Internal problem ID [8778]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
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)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{x}+\frac {c_{2} \left (-x^{3} {\mathrm e}^{x} \expIntegral \left (1, x\right )+x^{2}-x +2\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 40
DSolve[(-2 - 3*x)*y[x] - (-2*x + x^2)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x x-\frac {c_2 \left (e^x x^3 \text {Ei}(-x)+(x-1) x+2\right )}{6 x^2} \\ \end{align*}