Solving systems of Differential equations of $\vec{\phi} = A e^{\vec{\phi}}$

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I want to solve following systems of differential equation

\begin{align} \frac{d^2}{dt^2}\begin{pmatrix} \phi_1(t) \\ \phi_2(t) \end{pmatrix} = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} e^{\phi_1(t)} \\ e^{\phi_2(t)} \end{pmatrix} \end{align} where $a,b,c,d$ are constant.

Is there any way to solve this? Here I have difficulty of handling $e^{\phi_{1}(t)}$ and $e^{\phi_2{(t)}}$