84.1.5 problem 1.5

Internal problem ID [22069]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts
Problem number : 1.5
Date solved : Thursday, October 02, 2025 at 08:23:23 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 53

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

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {\textit {\_a}^{2}+2 \ln \left (\textit {\_a} \right )+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {\textit {\_a}^{2}+2 \ln \left (\textit {\_a} \right )+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 41

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

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+2 \left (\frac {K[1]^2}{2}+\log (K[1])\right )}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]

✗ Sympy

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

Timed Out