90.20.1 problem 1

Internal problem ID [25296]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:59:39 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*} y^{\prime \prime }+y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 3.986 (sec). Leaf size: 34

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(t), t) + Derivative(y(t), (t, 2))/y(t) cannot be so