Internal problem ID [9589]
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]]
\[ \boxed {\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 x} \left (x -1\right )+c_{2} \left (-195 \left (x -1\right ) {\mathrm e}^{2 x -5} \operatorname {Ei}_{1}\left (5 x -5\right )+\left (x +44\right ) {\mathrm e}^{-3 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.514 (sec). Leaf size: 52
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]
\[ y(x)\to 39 c_2 e^{2 x-5} (x-1) \operatorname {ExpIntegralEi}(5-5 x)+c_1 \left (-e^{2 x}\right ) (x-1)+\frac {1}{5} c_2 e^{-3 x} (x+44) \]