8.6.10 problem 10

Internal problem ID [780]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 10
Date solved : Saturday, March 29, 2025 at 10:22:22 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 13

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

\[ y = \tan \left (\frac {1}{3} x^{3}+c_1 +x \right ) \]

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 17

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

\[ y(x)\to \tan \left (\frac {x^3}{3}+x+c_1\right ) \]

✓ Sympy. Time used: 0.587 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \tan {\left (C_{1} + \frac {x^{3}}{3} + x \right )} \]