Internal problem ID [2409]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(2*x-1)*diff(y(x),x)+x*(x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{2} \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (-2+2 x -\frac {2}{3} x^{3}+\frac {5}{12} x^{4}-\frac {3}{20} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 59
AsymptoticDSolveValue[x^2*y''[x]+x*(2*x-1)*y'[x]+x*(x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {5 x^4}{24}+\frac {x^3}{3}-x+1\right )+c_2 \left (\frac {x^6}{24}-\frac {x^5}{6}+\frac {x^4}{2}-x^3+x^2\right ) \]