Internal problem ID [2400]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page
739
Problem number: Problem 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+4 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve(diff(y(x),x$2)+2*diff(y(x),x)+4*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {2}{3} x^{3}+\frac {1}{3} x^{4}-\frac {2}{15} x^{5}\right ) y \relax (0)+\left (x -x^{2}+\frac {2}{3} x^{3}-\frac {2}{3} x^{4}+\frac {7}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 61
AsymptoticDSolveValue[y''[x]+2*y'[x]+4*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {2 x^5}{15}+\frac {x^4}{3}-\frac {2 x^3}{3}+1\right )+c_2 \left (\frac {7 x^5}{15}-\frac {2 x^4}{3}+\frac {2 x^3}{3}-x^2+x\right ) \]