Internal problem ID [7300]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
✗ 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: 0.032 (sec). Leaf size: 113
AsymptoticDSolveValue[y'[x]+y[x]==1/x,y[x],{x,0,5}]
\[ y(x)\to \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \left (\frac {x^6}{2160}+\frac {x^5}{600}+\frac {x^4}{96}+\frac {x^3}{18}+\frac {x^2}{4}+x+\log (x)\right )+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]