4.2.26 problem 26

Internal problem ID [1154]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 04:24:44 AM
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: 0.094 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.137 (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]
 

\begin{align*} y(x)&\to \tan (x (x+2)) \end{align*}

✓ Sympy. Time used: 0.382 (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)
 

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