Internal problem ID [4514]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 49
Order:=6; dsolve((x^2-5*x+6)*diff(y(x),x$2)-3*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{12} x^{2}+\frac {5}{216} x^{3}+\frac {5}{324} x^{4}+\frac {11}{1296} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{9} x^{3}+\frac {5}{108} x^{4}+\frac {29}{1080} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(x^2-5*x+6)*y''[x]-3*x*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {29 x^5}{1080}+\frac {5 x^4}{108}+\frac {x^3}{9}+x\right )+c_1 \left (\frac {11 x^5}{1296}+\frac {5 x^4}{324}+\frac {5 x^3}{216}+\frac {x^2}{12}+1\right ) \]