56.1.46 problem 46

Internal problem ID [8758]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 46
Date solved : Monday, January 27, 2025 at 04:48:20 PM
CAS classification : [_quadrature]

\begin{align*} f^{\prime }&=\frac {1}{f} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(diff(f(x),x)=f(x)^(-1),f(x), singsol=all)
 

\begin{align*} f &= \sqrt {c_{1} +2 x} \\ f &= -\sqrt {c_{1} +2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 38

DSolve[D[ f[x],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*}