Internal problem ID [11885]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.1. Exercises page
232
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime } x -4 y=0} \] 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(diff(y(x),x$2)+8*x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (-2 x^{4}+2 x^{2}+1\right ) y \left (0\right )+\left (x -\frac {2}{3} x^{3}+\frac {2}{3} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[y''[x]+8*x*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {2 x^5}{3}-\frac {2 x^3}{3}+x\right )+c_1 \left (-2 x^4+2 x^2+1\right ) \]