Internal problem ID [4528]
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: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-x y-\sin \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
Order:=6; dsolve(diff(y(x),x)-x*y(x)=sin(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) y \relax (0)+\frac {x^{2}}{2}+\frac {x^{4}}{12}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
AsymptoticDSolveValue[y'[x]-x*y[x]==Sin[x],y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{12}+\frac {x^2}{2}+c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right ) \]