Internal problem ID [6518]
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]]
\[ \boxed {\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (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);
\[ y \left (x \right ) = c_{1} x \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (x +\operatorname {O}\left (x^{6}\right )\right ) \ln \left (x \right ) c_{2} +\left (1-x +\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 20
AsymptoticDSolveValue[(x^2-x)*y''[x]-x*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 (-3 x+x \log (x)+1) \]