88.10.5 problem 5

Internal problem ID [24040]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:55:04 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 24

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

\[ y = \frac {\tanh \left (\frac {\left (c_2 +x \right ) \sqrt {6}}{2 c_1}\right ) \sqrt {6}}{3 c_1} \]

✓ Mathematica. Time used: 7.16 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+3*y[x]*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {\frac {2}{3}} \sqrt {c_1} \tanh \left (\sqrt {\frac {3}{2}} \sqrt {c_1} (x+c_2)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) + Derivative(y(x), (x, 2))/(3*y(x)) cannot b