Internal problem ID [8754]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1174.
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 }-2 x y^{\prime }+2 y-x^{5} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-x^5*ln(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{2}+c_{1} x^{2}+\frac {x^{5} \left (12 \ln \relax (x )-7\right )}{144} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 32
DSolve[-(x^5*Log[x]) + 2*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)+c_2 x^2+c_1 x \\ \end{align*}