Internal problem ID [426]
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 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {5 y^{\prime \prime }-2 y^{\prime } x +10 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve(5*diff(y(x),x$2)-2*x*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}+\frac {1}{10} x^{4}\right ) y \left (0\right )+\left (\frac {4}{375} x^{5}-\frac {4}{15} x^{3}+x \right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[5*y''[x]-2*x*y'[x]+10*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {4 x^5}{375}-\frac {4 x^3}{15}+x\right )+c_1 \left (\frac {x^4}{10}-x^2+1\right ) \]