Find a function $u(x, t)$ that satisfies the PDE egin{cases} u_{xx} = 0, \ 0 < x < 1 \ t > 0 \ u(0, t) = t^2 \ u(1, t) = 1 end{cases}

          Find a function $u(x, t)$ that satisfies the PDE egin{cases} u_{xx} = 0, \ 0 < x < 1 \ t > 0 \ u(0, t) = t^2 \ u(1, t) = 1 end{cases}

Added by Ian T.

James Stewart 8th Edition

Instant Answer

03/12/2023

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This can be done by taking the derivative of Urr with respect to t: Urr'(x,t) = Urr(x,t) - x*Urr(x,t-1) Show more…

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Find a function u(x,t) that satisfies the PDE uxx = 0, 0 < x < 1, t > 0, u(0,t) = t^2, u(1,t) = 1

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Find a function $u(x, t)$ that satisfies the PDE egin{cases} u_{xx} = 0, \ 0 < x < 1 \ t > 0 \ u(0, t) = t^2 \ u(1, t) = 1 end{cases}