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Physical Mathematics by Kevin Cahill

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7

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Integral equations

Differential equations when integrated become integral equations with built-in boundary conditions. Thus if we integrate the first-order ODE

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(7.1)

then we get the integral equation

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(7.2)

and the boundary condition u(a) = f(a) = u0.

With a little more effort, we may integrate the second-order ODE

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(7.3) ...

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