50.1.46 problem 46

Internal problem ID [10044]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 46
Date solved : Tuesday, September 30, 2025 at 06:50:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(f(x),x) = 1/f(x); 
dsolve(ode,f(x), singsol=all);
 

\begin{align*} f &= \sqrt {2 x +c_1} \\ f &= -\sqrt {2 x +c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 38

ode=D[ f[x],x]==f[x]^(-1); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
f = Function("f") 
ode = Eq(Derivative(f(x), x) - 1/f(x),0) 
ics = {} 
dsolve(ode,func=f(x),ics=ics)
 

\[ \left [ f{\left (x \right )} = - \sqrt {C_{1} + 2 x}, \ f{\left (x \right )} = \sqrt {C_{1} + 2 x}\right ] \]