44.1.55 problem 70

Internal problem ID [6930]
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 : Monday, January 27, 2025 at 02:37:12 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ y = 2 \tan \left (2 c_{1} +2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 28

DSolve[D[y[x],x]==y[x]^2+4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 \tan (2 (x+c_1)) \\ y(x)\to -2 i \\ y(x)\to 2 i \\ \end{align*}