Internal problem ID [2406]
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 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime } x^{2}+y x -2 \cos \relax (x )=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: 30
Order:=6; dsolve(diff(y(x),x$2)+2*x^2*diff(y(x),x)+x*y(x)=2*cos(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {x^{3}}{6}\right ) y \relax (0)+\left (x -\frac {1}{4} x^{4}\right ) D\relax (y )\relax (0)+x^{2}-\frac {x^{4}}{12}-\frac {x^{5}}{4}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 45
AsymptoticDSolveValue[y''[x]+2*x^2*y'[x]+x*y[x]==2*Cos[x],y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{4}-\frac {x^4}{12}+c_2 \left (x-\frac {x^4}{4}\right )+c_1 \left (1-\frac {x^3}{6}\right )+x^2 \]