38.1.55 problem 70

Internal problem ID [8216]
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 : 70
Date solved : Tuesday, September 30, 2025 at 05:18:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

\[ y = 2 \tan \left (2 x +2 c_1 \right ) \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+4}dK[1]\&\right ][x+c_1]\\ y(x)&\to -2 i\\ y(x)&\to 2 i \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = - 2 \tan {\left (C_{1} - 2 x \right )} \]