Internal problem ID [4781]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page
230
Problem number: 15 (x=1).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 54
Order:=6; dsolve((x^2-25)*diff(y(x),x$2)+2*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1+\frac {\left (x -1\right )^{2}}{48}+\frac {\left (x -1\right )^{3}}{864}+\frac {\left (x -1\right )^{4}}{1728}+\frac {29 \left (x -1\right )^{5}}{414720}\right ) y \relax (1)+\left (x -1+\frac {\left (x -1\right )^{2}}{24}+\frac {5 \left (x -1\right )^{3}}{216}+\frac {17 \left (x -1\right )^{4}}{6912}+\frac {41 \left (x -1\right )^{5}}{51840}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 87
AsymptoticDSolveValue[(x^2-25)*y''[x]+2*x*y'[x]+y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {29 (x-1)^5}{414720}+\frac {(x-1)^4}{1728}+\frac {1}{864} (x-1)^3+\frac {1}{48} (x-1)^2+1\right )+c_2 \left (\frac {41 (x-1)^5}{51840}+\frac {17 (x-1)^4}{6912}+\frac {5}{216} (x-1)^3+\frac {1}{24} (x-1)^2+x-1\right ) \]