60.9.35 problem 1890

Internal problem ID [11814]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1890
Date solved : Sunday, March 30, 2025 at 09:15:54 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d^{2}}{d t^{2}}x \left (t \right )&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2}\\ \frac {d^{2}}{d t^{2}}y \left (t \right )&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2} \end{align*}

✗ Maple

ode:=[diff(diff(x(t),t),t) = (3*cos(a*t+b)^2-1)*c^2*x(t)+3/2*c^2*y(t)*sin(2*a*t*b), diff(diff(y(t),t),t) = (3*sin(a*t+b)^2-1)*c^2*y(t)+3/2*c^2*x(t)*sin(2*a*t*b)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],{t,2}]==(3*Cos[a*t+b]^2-1)*c^2*x[t]+3/2*c^2*y[t]*Sin[2*(a*t*b)],D[y[t],{t,2}]==(3*Sin[a*t+b]^2-1)*c^2*y[t]+3/2*c^2*x[t]*Sin[2*(a*t*b)]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-c**2*(3*cos(a*t + b)**2 - 1)*x(t) - 3*c**2*y(t)*sin(2*a*b*t)/2 + Derivative(x(t), (t, 2)),0),Eq(-c**2*(3*sin(a*t + b)**2 - 1)*y(t) - 3*c**2*x(t)*sin(2*a*b*t)/2 + Derivative(y(t), (t, 2)),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

NotImplementedError :