56.5.10 problem 10

Internal problem ID [8971]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:25:37 PM
CAS classification : [_quadrature]

\begin{align*} y^{\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)=1/x,y(x),type='series',x=0);
 
\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 8

AsymptoticDSolveValue[D[y[x],x]==1/x,y[x],{x,0,"6"-1}]
 
\[ y(x)\to \log (x)+c_1 \]