Internal problem ID [8779]
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]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 32
dsolve(x^2*diff(diff(y(x),x),x)-x*(x+4)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{4} {\mathrm e}^{x}+c_{2} x \left ({\mathrm e}^{x} x^{3} \expIntegral \left (1, x\right )-x^{2}+x -2\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 40
DSolve[4*y[x] - x*(4 + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 e^x x^4-\frac {1}{6} c_1 x \left (e^x x^3 \text {Ei}(-x)+(x-1) x+2\right ) \\ \end{align*}