83.10.16 problem 16

Internal problem ID [21985]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter IV. First order differential equations of higher degree. Ex. XI at page 69
Problem number : 16
Date solved : Thursday, October 02, 2025 at 08:21:24 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 17

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

\begin{align*} y &= 0 \\ y &= \frac {\left (x -c_1 \right )^{2}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to \frac {1}{4} (x-c_1){}^2\\ y(x)&\to \frac {1}{4} (x+c_1){}^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} - \frac {C_{1} x}{2} + \frac {x^{2}}{4} \]