= Solution of a differential equation
= Solutions of a differential equation
{synonym}
A classical solution is a sufficiently differentiable <function> that satisfies a <differential equation> and any prescribed initial or boundary conditions. A <weak solution> instead satisfies an appropriate integral or distributional identity in a specified <function space>. For a smooth locally <Lipschitz continuous> vector field, an <ordinary differential equation> has a unique local solution for each initial state; this does not by itself ensure global existence or boundedness.
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