76.30.2 problem 2

Internal problem ID [17819]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 7. Nonlinear Differential Equations and Stability. Section 7.1 (Autonomous Systems and Stability). Problems at page 464
Problem number : 2
Date solved : Monday, March 31, 2025 at 04:33:19 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=1+5 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=1-6 x \left (t \right )^{2} \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 25

ode:=[diff(x(t),t) = 1+5*y(t), diff(y(t),t) = 1-6*x(t)^2]; 
dsolve(ode);
 

\begin{align*} \left \{x \left (t \right ) &= -\frac {\operatorname {WeierstrassP}\left (t +c_1 , 50, c_2\right )}{5}\right \} \\ \left \{y \left (t \right ) &= \frac {\frac {d}{d t}x \left (t \right )}{5}-\frac {1}{5}\right \} \\ \end{align*}

✓ Mathematica. Time used: 0.574 (sec). Leaf size: 923

ode={D[x[t],t]==1+5*y[t],D[y[t],t]==1-6*x[t]^2}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-5*y(t) + Derivative(x(t), t) - 1,0),Eq(6*x(t)**2 + Derivative(y(t), t) - 1,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)