15.3 problem 3

Internal problem ID [11904]

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: 3.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y=0} \] With the expansion point for the power series method at \(x = 0\).

✗ Solution by Maple

Order:=6; 
dsolve((x^4-2*x^3+x^2)*diff(y(x),x$2)+2*(x-1)*diff(y(x),x)+x^2*y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 71

AsymptoticDSolveValue[(x^4-2*x^3+x^2)*y''[x]+2*(x-1)*y'[x]+x^2*y[x]==0,y[x],{x,0,5}]
                                                                                    
                                                                                    
 

\[ y(x)\to c_1 \left (\frac {3 x^5}{10}+\frac {x^4}{4}+\frac {x^3}{6}+1\right )+c_2 e^{-2/x} \left (-\frac {429 x^5}{5}+\frac {91 x^4}{4}-\frac {31 x^3}{6}+3 x^2+1\right ) x^4 \]