87.7.9 problem 12

Internal problem ID [23350]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 57
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:39:26 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-2*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-c_1 +\tan \left (\frac {c_2 +x}{c_1}\right )}{c_1} \]

✓ Mathematica. Time used: 47.857 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -1+\sqrt {-1+c_1} \tan \left (\sqrt {-1+c_1} (x+c_2)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x)*Derivative(y(x), x) - 2*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))/(2*(y(x) + 1)) ca