82.8.25 problem 36-26

Internal problem ID [21896]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-26
Date solved : Thursday, October 02, 2025 at 08:05:50 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=\sin \left (x \left (t \right )\right )-4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=\sin \left (2 x \left (t \right )\right )-5 y \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = sin(x(t))-4*y(t), diff(y(t),t) = sin(2*x(t))-5*y(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==Sin[x[t]]-4*y[t],D[y[t],t]==Sin[2*x[t]]-5*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(4*y(t) - sin(x(t)) + Derivative(x(t), t),0),Eq(5*y(t) - sin(2*x(t)) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out