Internal problem ID [739]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number: 6. case \(x_0=0\).
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 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 49
Order:=6; dsolve((x^2-2*x-3)*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {2}{3} x^{2}-\frac {4}{27} x^{3}+\frac {16}{81} x^{4}-\frac {1}{9} x^{5}\right ) y \relax (0)+\left (x +\frac {5}{18} x^{3}-\frac {5}{54} x^{4}+\frac {7}{72} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(x^2-2*x-3)*y''[x]+x*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {7 x^5}{72}-\frac {5 x^4}{54}+\frac {5 x^3}{18}+x\right )+c_1 \left (-\frac {x^5}{9}+\frac {16 x^4}{81}-\frac {4 x^3}{27}+\frac {2 x^2}{3}+1\right ) \]