76.1.34 problem 34

Internal problem ID [17262]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 34
Date solved : Monday, March 31, 2025 at 03:47:47 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 \left (1+x \right ) \left (1+y^{2}\right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.089 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.22 (sec). Leaf size: 11

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

\[ y(x)\to \tan (x (x+2)) \]

✓ Sympy. Time used: 0.543 (sec). Leaf size: 10

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

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