44.1.16 problem 18

Internal problem ID [6891]
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 : Monday, January 27, 2025 at 02:34:09 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

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

\[ y = 5 \tan \left (5 x +5 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 28

DSolve[D[y[x],x]==25+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 5 \tan (5 (x+c_1)) \\ y(x)\to -5 i \\ y(x)\to 5 i \\ \end{align*}