56.5.13 problem 13

Internal problem ID [8974]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 13
Date solved : Monday, January 27, 2025 at 05:25:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 148

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

\[ y(x)\to x \left (-\frac {x^6}{5040}+\frac {x^4}{120}-\frac {x^2}{6}+1\right ) \left (-\frac {x^6}{4320}+\frac {x^4}{96}-\frac {x^2}{4}+\log (x)\right )+c_1 \left (-\frac {x^6}{720}+\frac {x^4}{24}-\frac {x^2}{2}+1\right )+c_2 x \left (-\frac {x^6}{5040}+\frac {x^4}{120}-\frac {x^2}{6}+1\right )+\left (-\frac {x^5}{600}+\frac {x^3}{18}-x\right ) \left (-\frac {x^6}{720}+\frac {x^4}{24}-\frac {x^2}{2}+1\right ) \]