36.6.18 problem 21

Internal problem ID [6379]
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
Date solved : Monday, January 27, 2025 at 01:58:30 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-y x&=\sin \left (x \right ) \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 34

Order:=6; 
dsolve(diff(y(x),x)-x*y(x)=sin(x),y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) y \left (0\right )+\frac {x^{2}}{2}+\frac {x^{4}}{12}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 37

AsymptoticDSolveValue[D[y[x],x]-x*y[x]==Sin[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^4}{12}+\frac {x^2}{2}+c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right ) \]