81.13.3 problem 17-3

Internal problem ID [21677]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 17. Reduction of Order. Page 420
Problem number : 17-3
Date solved : Thursday, October 02, 2025 at 07:59:50 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-4 y&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 15

ode:=diff(y(x),x)^2-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 38

ode=D[y[x],x]^2-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.181 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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