Internal problem ID [8834]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1254.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve((x^2+x-2)*diff(diff(y(x),x),x)+(x^2-x)*diff(y(x),x)-(6*x^2+7*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{2 x} \left (x -1\right )+c_{2} \left (195 \,{\mathrm e}^{-5+2 x} \left (x -1\right ) \expIntegral \left (1, 5 x -5\right )-{\mathrm e}^{-3 x} \left (x +44\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 49
DSolve[(-7*x - 6*x^2)*y[x] + (-x + x^2)*y'[x] + (-2 + x + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} c_2 e^{-3 x} (x+44)-e^{2 x-5} (x-1) \left (e^5 c_1-39 c_2 \text {Ei}(5-5 x)\right ) \\ \end{align*}