Internal problem ID [1241]
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: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x^{5}+6 y x^{4}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
Order:=6; dsolve(diff(y(x),x$2)+x^5*diff(y(x),x)+6*x^4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )+D\left (y \right )\left (0\right ) x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 10
AsymptoticDSolveValue[y''[x]+x^5*y'[x]+6*x^4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 \]