52.1.14 problem 14

Internal problem ID [10385]
Book : Second order enumerated odes
Section : section 1
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 07:22:52 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)+diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (c_1 x +c_2 \right ) \]

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 15

ode=D[y[x],{x,2}]+(D[y[x],x])^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x-c_1)+c_2 \end{align*}

✓ Sympy. Time used: 0.312 (sec). Leaf size: 8

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

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