Internal problem ID [724]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number: 17.
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 +2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = -1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(0) = 4, D(y)(0) = -1],y(x),type='series',x=0);
\[ y \relax (x ) = 4-x -4 x^{2}+\frac {1}{2} x^{3}+\frac {4}{3} x^{4}-\frac {1}{8} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{y''[x]+x*y'[x]+2*y[x]==0,{y[0]==4,y'[0]==-1}},y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{8}+\frac {4 x^4}{3}+\frac {x^3}{2}-4 x^2-x+4 \]