3.7.24 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 : Tuesday, September 30, 2025 at 04:21:20 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*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 6

ode:=diff(y(x),x) = 1+y(x)^2; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 7

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

\begin{align*} y(x)&\to \tan (x) \end{align*}

✓ Sympy. Time used: 0.218 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**2 + Derivative(y(x), x) - 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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