Internal problem ID [441]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number: problem 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{3}+1\right ) y^{\prime \prime }+y x^{4}=0} \] 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((1+x^3)*diff(y(x),x$2)+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[(1+x^3)*y''[x]+x^4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 \]