Internal problem ID [4783]
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: 16 (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}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
Order:=6; dsolve((x^2-2*x+10)*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1+\frac {2 \left (x -1\right )^{2}}{9}-\frac {2 \left (x -1\right )^{3}}{243}+\frac {\left (x -1\right )^{4}}{4374}+\frac {22 \left (x -1\right )^{5}}{98415}\right ) y \relax (1)+\left (x -1-\frac {\left (x -1\right )^{2}}{18}+\frac {14 \left (x -1\right )^{3}}{243}-\frac {7 \left (x -1\right )^{4}}{4374}-\frac {154 \left (x -1\right )^{5}}{98415}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 87
AsymptoticDSolveValue[(x^2-2*x+10)*y''[x]+x*y'[x]-4*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {22 (x-1)^5}{98415}+\frac {(x-1)^4}{4374}-\frac {2}{243} (x-1)^3+\frac {2}{9} (x-1)^2+1\right )+c_2 \left (-\frac {154 (x-1)^5}{98415}-\frac {7 (x-1)^4}{4374}+\frac {14}{243} (x-1)^3-\frac {1}{18} (x-1)^2+x-1\right ) \]