Internal problem ID [9529]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1199.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (4+x \right ) y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x^2*diff(diff(y(x),x),x)-x*(x+4)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left ({\mathrm e}^{x} \operatorname {expIntegral}_{1}\left (x \right ) c_{2} x^{3}+{\mathrm e}^{x} x^{3} c_{1} -c_{2} \left (x^{2}-x +2\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 41
DSolve[4*y[x] - x*(4 + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^x x^4-\frac {1}{6} c_1 x \left (e^x x^3 \operatorname {ExpIntegralEi}(-x)+x^2-x+2\right ) \]