68.1.4 problem 5

Internal problem ID [17071]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 5
Date solved : Thursday, October 02, 2025 at 01:42:37 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.049 (sec). Leaf size: 17

ode:=diff(y(x),x)^2+y(x) = 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: 42

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

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

✓ Sympy. Time used: 0.224 (sec). Leaf size: 31

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)
 

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