Solve the following PDE for u(x,y). u_{yy} - 16u = 0 a. u(x,y) = c_1(y)e^{4x} + c_2(y)e^{-4x} b. u(x,y) = c_1 cos(4y) + c_2 sin(4y) c. u(x,y) = c_1(y) cos(4x) + c_2(y) sin(4x) d. u(x,y) = c_1(x)e^{4y} + c_2(x)e^{-4y} e. u(x,y) = c_1(x) cos(4y) + c_2(x) sin(4y)
Added by Dalton G.
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Let's check each solution: a) For the first solution, we have: $$u_{yy}(x,y) = C_1''(y)e^x + C_2''(y)e^b$$ Substituting this into the PDE, we get: $$C_1''(y)e^x + C_2''(y)e^b - 16(C_1(y)e^x + C_2(y)e^b) = 0$$ This does not satisfy the PDE for all values of Show more…
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