Question

(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the heat equation with homogeneous boundary conditions ,0 < z < 2, t > 0 v(0, t) 0, v(2, t)0,t >0 v(x,0)-x(2 -x) - S(x),0<a < 2 Using the substitution u-v S tu ôu ot So the steady-state solution S must satisfy the IVP (DE first, then IC's) S(0) S(2) Therefore S(x)- and v(r,t) be with heat equation is Therefore the solution of nonhomogeneous u(z,t) = u+ S =

Answer 1

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