60.9.35 problem 1890

Internal problem ID [11889]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1890
Date solved : Monday, January 27, 2025 at 11:44:12 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*}

Solution by Maple

dsolve([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(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))],singsol=all)
 
\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{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)]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved