Internal problem ID [11891]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
Order:=6; dsolve((x-1)*diff(y(x),x$2)-(3*x-2)*diff(y(x),x)+2*x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{3} x^{3}+\frac {1}{3} x^{4}+\frac {11}{60} x^{5}\right ) y \left (0\right )+\left (x +x^{2}+\frac {1}{2} x^{3}+\frac {1}{6} x^{4}+\frac {1}{24} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 59
AsymptoticDSolveValue[(x-1)*y''[x]-(3*x-2)*y'[x]+2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {11 x^5}{60}+\frac {x^4}{3}+\frac {x^3}{3}+1\right )+c_2 \left (\frac {x^5}{24}+\frac {x^4}{6}+\frac {x^3}{2}+x^2+x\right ) \]