Internal problem ID [738]
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: 5. case \(x_0=4\).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+6 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 4\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 54
Order:=6; dsolve(diff(y(x),x$2)+4*diff(y(x),x)+6*x*y(x)=0,y(x),type='series',x=4);
\[ y \relax (x ) = \left (1-12 \left (x -4\right )^{2}+15 \left (x -4\right )^{3}+9 \left (x -4\right )^{4}-\frac {108 \left (x -4\right )^{5}}{5}\right ) y \relax (4)+\left (x -4-2 \left (x -4\right )^{2}-\frac {4 \left (x -4\right )^{3}}{3}+\frac {29 \left (x -4\right )^{4}}{6}-\frac {5 \left (x -4\right )^{5}}{3}\right ) D\relax (y )\relax (4)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 79
AsymptoticDSolveValue[y''[x]+4*y'[x]+6*x*y[x]==0,y[x],{x,4,5}]
\[ y(x)\to c_1 \left (-\frac {108}{5} (x-4)^5+9 (x-4)^4+15 (x-4)^3-12 (x-4)^2+1\right )+c_2 \left (-\frac {5}{3} (x-4)^5+\frac {29}{6} (x-4)^4-\frac {4}{3} (x-4)^3-2 (x-4)^2+x-4\right ) \]