Internal problem ID [6337]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {f^{\prime }-\frac {1}{f}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(f(x),x)=f(x)^(-1),f(x), singsol=all)
\begin{align*} f \relax (x ) = \sqrt {2 x +c_{1}} \\ f \relax (x ) = -\sqrt {2 x +c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 38
DSolve[f'[x]==f[x]^(-1),f[x],x,IncludeSingularSolutions -> True]
\begin{align*} f(x)\to -\sqrt {2} \sqrt {x+c_1} \\ f(x)\to \sqrt {2} \sqrt {x+c_1} \\ \end{align*}