Internal problem ID [4532]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y-\cos \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
Order:=6; dsolve((1+x^2)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=cos(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (-\frac {1}{2} x^{2}+1+\frac {1}{24} x^{4}\right ) y \relax (0)+D\relax (y )\relax (0) x +\frac {x^{2}}{2}-\frac {x^{4}}{12}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 41
AsymptoticDSolveValue[(1+x^2)*y''[x]-x*y'[x]+y[x]==Cos[x],y[x],{x,0,5}]
\[ y(x)\to -\frac {x^4}{12}+\frac {x^2}{2}+c_1 \left (\frac {x^4}{24}-\frac {x^2}{2}+1\right )+c_2 x \]