85.27.13 problem 13

Internal problem ID [22605]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 13
Date solved : Thursday, October 02, 2025 at 08:54:56 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+diff(y(x),x)^2 = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x +\ln \left (-\frac {c_1 \,{\mathrm e}^{2 x}}{2}+\frac {c_2}{2}\right ) \]

✓ Mathematica. Time used: 0.253 (sec). Leaf size: 48

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

\begin{align*} y(x)&\to -\frac {1}{2} \log \left (e^{2 x}\right )+\log \left (e^{2 x}+e^{2 c_1}\right )+c_2\\ y(x)&\to \frac {1}{2} \log \left (e^{2 x}\right )+c_2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out