85.28.6 problem 6

Internal problem ID [22613]
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. B Exercises at page 60
Problem number : 6
Date solved : Thursday, October 02, 2025 at 08:55:03 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 39

ode:=1+diff(y(x),x)^2+y(x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 8.227 (sec). Leaf size: 83

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

\begin{align*} y(x)&\to -\sqrt {e^{2 c_1}-(x+c_2){}^2}\\ y(x)&\to \sqrt {e^{2 c_1}-(x+c_2){}^2}\\ y(x)&\to -\sqrt {-(x+c_2){}^2}\\ y(x)&\to \sqrt {-(x+c_2){}^2} \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 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(-y(x)*Derivative(y(x), (x, 2)) - 1) + Derivative(y(x), x)