Internal problem ID [11902]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.2 (Frobenius).
Exercises page 251
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 44
Order:=6; dsolve((x^2-3*x)*diff(y(x),x$2)+(x+2)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {5}{3}} \left (1+\frac {17}{36} x +\frac {1241}{7128} x^{2}+\frac {80665}{1347192} x^{3}+\frac {972725}{48498912} x^{4}+\frac {5797441}{872980416} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {1}{2} x -\frac {1}{2} x^{2}-\frac {5}{24} x^{3}-\frac {25}{336} x^{4}-\frac {17}{672} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 85
AsymptoticDSolveValue[(x^2-3*x)*y''[x]+(x+2)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {17 x^5}{672}-\frac {25 x^4}{336}-\frac {5 x^3}{24}-\frac {x^2}{2}-\frac {x}{2}+1\right )+c_1 \left (\frac {5797441 x^5}{872980416}+\frac {972725 x^4}{48498912}+\frac {80665 x^3}{1347192}+\frac {1241 x^2}{7128}+\frac {17 x}{36}+1\right ) x^{5/3} \]