44.2.30 problem 30

Internal problem ID [6962]
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. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:38:50 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 6

dsolve([diff(y(x),x)=1+y(x)^2,y(0) = 0],y(x), singsol=all)
 

\[ y = \tan \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 7

DSolve[{D[y[x],x]==1+y[x]^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan (x) \]