Internal problem ID [13605]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.5 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
Order:=6; dsolve((4+x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )+\left (x -\frac {1}{12} x^{3}+\frac {1}{80} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 25
AsymptoticDSolveValue[(4+x^2)*y''[x]+2*x*y'[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{80}-\frac {x^3}{12}+x\right )+c_1 \]