2.3.19 problem 20

Internal problem ID [695]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:06:20 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.077 (sec). Leaf size: 12

ode:=diff(y(x),x) = 3*x^2*(1+y(x)^2); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \tan \left (x^{3}+\frac {\pi }{4}\right ) \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 15

ode=D[y[x],x]== 3*x^2*(1+y[x]^2); 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \tan \left (x^3+\frac {\pi }{4}\right ) \end{align*}

✓ Sympy. Time used: 0.217 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2*(y(x)**2 + 1) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \tan {\left (x^{3} + \frac {\pi }{4} \right )} \]