6.1.14 problem 5(c)

Internal problem ID [1532]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 5(c)
Date solved : Tuesday, September 30, 2025 at 04:35:27 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.073 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.113 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \tan \left (\frac {x^2}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.186 (sec). Leaf size: 8

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

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