Internal problem ID [6551]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {1}{x}=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$2)=1/x,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 17
AsymptoticDSolveValue[y''[x]==1/x,y[x],{x,0,5}]
\[ y(x)\to -x+x \log (x)+c_2 x+c_1 \]