56.5.7 problem 7

Internal problem ID [8968]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:25:34 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\frac {1}{x} \end{align*}

Using series method with expansion around

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

Solution by Maple

Order:=6; 
dsolve(diff(y(x),x)+y(x)=1/x,y(x),type='series',x=0);
 
\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 113

AsymptoticDSolveValue[D[y[x],x]+y[x]==1/x,y[x],{x,0,"6"-1}]
 
\[ y(x)\to \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \left (\frac {x^6}{2160}+\frac {x^5}{600}+\frac {x^4}{96}+\frac {x^3}{18}+\frac {x^2}{4}+x+\log (x)\right )+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]