56.5.8 problem 8

Internal problem ID [8969]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:25:35 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\frac {1}{x^{2}} \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^2,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 122

AsymptoticDSolveValue[D[y[x],x]+y[x]==1/x^2,y[x],{x,0,"6"-1}]
 

\[ y(x)\to \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \left (\frac {x^6}{2160}+\frac {x^5}{1800}+\frac {x^4}{480}+\frac {x^3}{72}+\frac {x^2}{12}+\frac {x}{2}-\frac {1}{x}+\log (x)\right )+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]