67.2.6 problem 3.4 f

Internal problem ID [16316]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 f
Date solved : Thursday, October 02, 2025 at 01:18:44 PM
CAS classification : [_quadrature]

\begin{align*} y^{3}-25 y+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

ode:=y(x)^3-25*y(x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_1 +1}} \\ y &= \frac {5}{\sqrt {25 \,{\mathrm e}^{-50 x} c_1 +1}} \\ \end{align*}

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 53

ode=y[x]^3-25*y[x]+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-5) K[1] (K[1]+5)}dK[1]\&\right ][-x+c_1]\\ y(x)&\to -5\\ y(x)&\to 0\\ y(x)&\to 5 \end{align*}

✓ Sympy. Time used: 2.016 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**3 - 25*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 5 \sqrt {- \frac {e^{50 x}}{C_{1} - e^{50 x}}}, \ y{\left (x \right )} = 5 \sqrt {- \frac {e^{50 x}}{C_{1} - e^{50 x}}}\right ] \]