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Solving differential equations and specifying initial conditions

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Given an equation, can you solve for the derivatives of certain quantities in terms of the other variables? For example in the following equation when I try to solve for diff(y(t)) Matlab is unable to find an explicit solution but diff(y(t)) is equal to diff(x(t)), so if the value of diff(x(t)) can be specified diff(y(t)) could be found. How can you specify appropriate conditions such as the value of diff(x(t)) to solve for the derivatives of other quantities?
syms x(t) y(t)
eq1 = x == y+2;

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