Internal problem ID [2407]
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 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } x -4 y-6 \,{\mathrm e}^{x}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 42
Order:=6; dsolve(diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=6*exp(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+2 x^{2}+\frac {1}{3} x^{4}\right ) y \relax (0)+\left (x +\frac {1}{2} x^{3}+\frac {1}{40} x^{5}\right ) D\relax (y )\relax (0)+3 x^{2}+x^{3}+\frac {3 x^{4}}{4}+\frac {x^{5}}{10}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 62
AsymptoticDSolveValue[y''[x]+x*y'[x]-4*y[x]==6*Exp[x],y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{10}+\frac {3 x^4}{4}+x^3+3 x^2+c_2 \left (\frac {x^5}{40}+\frac {x^3}{2}+x\right )+c_1 \left (\frac {x^4}{3}+2 x^2+1\right ) \]