Internal problem ID [737]
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 \(x_0=0\).
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 \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
Order:=6; dsolve(diff(y(x),x$2)+4*diff(y(x),x)+6*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-x^{3}+x^{4}-\frac {4}{5} x^{5}\right ) y \relax (0)+\left (x -2 x^{2}+\frac {8}{3} x^{3}-\frac {19}{6} x^{4}+\frac {47}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 55
AsymptoticDSolveValue[y''[x]+4*y'[x]+6*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {4 x^5}{5}+x^4-x^3+1\right )+c_2 \left (\frac {47 x^5}{15}-\frac {19 x^4}{6}+\frac {8 x^3}{3}-2 x^2+x\right ) \]