Internal problem ID [6519]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 34
Order:=6; dsolve((x^2-x)*diff(y(x), x$2)-x*diff(y(x), x)+y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \ln \relax (x ) \left (x +\mathrm {O}\left (x^{6}\right )\right ) c_{2}+c_{1} x \left (1+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-x +\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 20
AsymptoticDSolveValue[(x^2-x)*y''[x]-x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 (-3 x+x \log (x)+1) \]