Internal problem ID [1239]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 11
Order:=6; dsolve((1+x^8)*diff(y(x),x$2)-16*x^7*diff(y(x),x)+72*x^6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+D\relax (y )\relax (0) x \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 10
AsymptoticDSolveValue[(1+x^8)*y''[x]-16*x^7*y'[x]+72*x^6*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 \]