15.18.16 problem 16

Internal problem ID [3259]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 16
Date solved : Sunday, March 30, 2025 at 01:25:27 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = diff(y(x),x)^2+diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (-c_1 \,{\mathrm e}^{x}-c_2 \right ) \]

✓ Mathematica. Time used: 1.869 (sec). Leaf size: 31

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

\begin{align*} y(x)\to c_2-\log \left (-1+e^{x+c_1}\right ) \\ y(x)\to c_2-i \pi \\ \end{align*}

✓ Sympy. Time used: 0.859 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} - \log {\left (C_{2} + e^{x} \right )} \]