56.5.11 problem 11

Internal problem ID [8972]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:25:37 PM
CAS classification : [[_2nd_order, _quadrature]]

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 17

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

\[ y(x)\to -x+x \log (x)+c_2 x+c_1 \]