Internal problem ID [1240]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} 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: 14
Order:=6; dsolve((1-x^6)*diff(y(x),x$2)-12*x^5*diff(y(x),x)-30*x^4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 10
AsymptoticDSolveValue[(1-x^6)*y''[x]-12*x^5*y'[x]-30*x^4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 \]