35.9.1 problem 1, using series method

Internal problem ID [6236]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 1, using series method
Date solved : Monday, January 27, 2025 at 01:49:44 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=y x +y \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

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

\[ y = c_{1} x \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 38

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

\[ y(x)\to c_1 x \left (\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right ) \]