Internal problem ID [4533]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }+2 y-\cos \relax (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: 33
Order:=6; dsolve(diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=cos(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (-x^{2}+1\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+\frac {x^{2}}{2}-\frac {x^{4}}{24}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 47
AsymptoticDSolveValue[y''[x]-x*y'[x]+2*y[x]==Cos[x],y[x],{x,0,5}]
\[ y(x)\to -\frac {x^4}{24}+\frac {x^2}{2}+c_1 \left (1-x^2\right )+c_2 \left (-\frac {x^5}{120}-\frac {x^3}{6}+x\right ) \]