38.1.43 problem 45

Internal problem ID [8204]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 45
Date solved : Tuesday, September 30, 2025 at 05:18:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 38

ode=D[y[x],x]^2==4*y[x]; 
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: 0.176 (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)
 

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