Internal problem ID [2393]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page
739
Problem number: Problem 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } x +3 y=0} \end {gather*} 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)+x*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{2} x^{2}+\frac {5}{8} x^{4}\right ) y \relax (0)+\left (x -\frac {2}{3} x^{3}+\frac {1}{5} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[x]+x*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{5}-\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {5 x^4}{8}-\frac {3 x^2}{2}+1\right ) \]