38.1.16 problem 18

Internal problem ID [8177]
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 : 18
Date solved : Tuesday, September 30, 2025 at 05:18:09 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=25+y^{2} \end{align*}

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

ode:=diff(y(x),x) = 25+y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 5 \tan \left (5 x +5 c_1 \right ) \]

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

ode=D[y[x],x]==25+y[x]^2; 
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+25}dK[1]\&\right ][x+c_1]\\ y(x)&\to -5 i\\ y(x)&\to 5 i \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 + Derivative(y(x), x) - 25,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 5 \tan {\left (C_{1} - 5 x \right )} \]