85.6.3 problem 4 (b)

Internal problem ID [22453]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. C Exercises at page 22
Problem number : 4 (b)
Date solved : Thursday, October 02, 2025 at 08:39:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 19

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

\begin{align*} y &= -i x +c_1 \\ y &= i x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to c_1-i x\\ y(x)&\to i x+c_1 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 14

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

\[ \left [ y{\left (x \right )} = C_{1} - i x, \ y{\left (x \right )} = C_{1} + i x\right ] \]