Internal problem ID [723]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 3] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(2+x^2)*diff(y(x),x$2)-x*diff(y(x),x)+4*y(x)=0,y(0) = -1, D(y)(0) = 3],y(x),type='series',x=0);
\[ y \relax (x ) = -1+3 x +x^{2}-\frac {3}{4} x^{3}-\frac {1}{6} x^{4}+\frac {21}{160} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 32
AsymptoticDSolveValue[{(2+x^2)*y''[x]-x*y'[x]+4*y[x]==0,{y[0]==-1,y'[0]==3}},y[x],{x,0,5}]
\[ y(x)\to \frac {21 x^5}{160}-\frac {x^4}{6}-\frac {3 x^3}{4}+x^2+3 x-1 \]