9.7.24 problem problem 26(a)

Internal problem ID [1065]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 26(a)
Date solved : Monday, January 27, 2025 at 04:32:46 AM
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: 0.004 (sec). Leaf size: 7

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

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