85.33.58 problem 58

Internal problem ID [22681]
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 65
Problem number : 58
Date solved : Thursday, October 02, 2025 at 09:06:21 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 33

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

\begin{align*} y &= 0 \\ y &= \sqrt {2 c_1 x +2 c_2} \\ y &= -\sqrt {2 c_1 x +2 c_2} \\ \end{align*}

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 20

ode=y[x]*D[y[x],{x,2}]+D[y[x],{x,1}]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 \sqrt {2 x-c_1} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-y(x)*Derivative(y(x), (x, 2))) + Derivative(y(x), x) cann