49.3.10 problem 14(b)

Internal problem ID [7610]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 14(b)
Date solved : Monday, January 27, 2025 at 03:07:26 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: 0.019 (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: 0.004 (sec). Leaf size: 7

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

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