Internal problem ID [6548]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\frac {1}{x^{2}}=0} \end {gather*} 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^2,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 122
AsymptoticDSolveValue[y'[x]+y[x]==1/x^2,y[x],{x,0,5}]
\[ y(x)\to \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \left (\frac {x^6}{2160}+\frac {x^5}{1800}+\frac {x^4}{480}+\frac {x^3}{72}+\frac {x^2}{12}+\frac {x}{2}-\frac {1}{x}+\log (x)\right )+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]