  Let $I$ be an ideal of the ring of Laurent polynomials
$K[x_1^{\pm1},\ldots,x_n^{\pm1}]$ with coefficients in a real-valued field
$(K,v)$. The fundamental theorem of tropical algebraic geometry states the
equality $\text{trop}(V(I))=V(\text{trop}(I))$ between the tropicalization
$\text{trop}(V(I))$ of the closed subscheme $V(I)\subset (K^*)^n$ and the
tropical variety $V(\text{trop}(I))$ associated to the tropicalization of the
ideal $\text{trop}(I)$.
  In this work we prove an analogous result for a differential ideal $G$ of the
ring of differential polynomials $K[[t]]\{x_1,\ldots,x_n\}$, where $K$ is an
uncountable algebraically closed field of characteristic zero. We define the
tropicalization $\text{trop}(\text{Sol}(G))$ of the set of solutions
$\text{Sol}(G)\subset K[[t]]^n$ of $G$, and the set of solutions associated to
the tropicalization of the ideal $\text{trop}(G)$. These two sets are linked by
a tropicalization morphism $\text{trop}:\text{Sol}(G)\longrightarrow
\text{Sol}(\text{trop}(G))$.
  We show the equality $\text{trop}(\text{Sol}(G))=\text{Sol}(\text{trop}(G))$,
answering a question raised by D. Grigoriev earlier this year.
