9.18.26 problem 26

Internal problem ID [3269]
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 : 26
Date solved : Tuesday, September 30, 2025 at 06:31:52 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 24

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

\[ y = -x -\frac {\ln \left (2\right )}{2}+\frac {\ln \left (-c_1 \,{\mathrm e}^{4 x}+c_2 \right )}{2} \]

✓ Mathematica. Time used: 0.251 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to -\frac {1}{4} \log \left (e^{4 x}\right )+\frac {1}{2} \log \left (e^{4 x}+e^{2 c_1}\right )+c_2\\ y(x)&\to \frac {1}{4} \log \left (e^{4 x}\right )+c_2 \end{align*}

✗ Sympy

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

Timed Out