# Prove a Solution to a Probability Distribution

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Suppose that u_1 and u_2 are solutions of the PDE

delta(u)/delta(t) + p(x, t)*delta(u)/delta(x) = 0

Show that u = (c_1)(u_1) + (c_2)(u_2) is also a solution to the PDE for any constants (c_1) and (c_2).

Note: This shows that equation (1) is linear. For those of you who have taken linear algebra, this also shows that the set of all solutions to the PDE (1) is in fact a vector subspace of the space of all differentiable functions, c^-1 (R x {t >= 0})

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