Internal problem ID [9469]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1890.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\relax (t )&=\left (3 \left (\cos ^{2}\left (a t +b \right )\right )-1\right ) c^{2} x \relax (t )+\frac {3 c^{2} y \relax (t ) \sin \left (2 a t b \right )}{2}\\ y^{\prime \prime }\relax (t )&=\left (3 \left (\sin ^{2}\left (a t +b \right )\right )-1\right ) c^{2} y \relax (t )+\frac {3 c^{2} x \relax (t ) \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))},{x(t), y(t)}, singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]==(3*Cos[a*t+b]^2-1)*c^2*x[t]+3/2*c^2*y[t]*Sin[2*(a*t*b)],y''[t]==(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