Internal problem ID [9635]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1307.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(x^3*diff(diff(y(x),x),x)+x*(x+1)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} {\mathrm e}^{\frac {1}{x}} \left (x +1\right ) \operatorname {expIntegral}_{1}\left (\frac {1}{x}\right )+c_{1} {\mathrm e}^{\frac {1}{x}} \left (x +1\right )-x c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 44
DSolve[-2*y[x] + x*(1 + x)*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-c_2 e^{\frac {1}{x}} (x+1) \operatorname {ExpIntegralEi}\left (-\frac {1}{x}\right )+c_1 e^{\frac {1}{x}} (x+1)-c_2 x}{x} \]