I want to possibly analytically solve the following system of differential equations.
$$ X'(t) = \left\langle \frac{3}{4}, \frac{\sqrt{3}}{4} \sin(t) , \frac{-\sqrt3}{4}\cos (t) \right\rangle \times X(t) $$
where $X(0) = \left\langle \frac{\sqrt3}{2}, 0, -\frac{1}{2} \right\rangle $ and the '$\times$' denotes the vector cross product.
I know how to solve a system of differential equations when it is of the form $X' = AX$ where $A$ is some $3 \times 3$ matrix. One finds the eigen values of the matrix $A$ and proceed from there as usual. Is it possible to express the above problem in that form?. Any hints on how I should proceed?