Use separation of variables to solve the PDE u_t − u = u_xx  0 ≤ x ≤ π/2 , t ≥ 0  boundary conditions ux(0, t) = 0 and u(π/2, t) = 0 initial conditions u(x, 0) = 1 − cos(4x)

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

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Q: Use separation of variables to solve the PDE u_t − u = u_xx  0 ≤ x ≤ π/2 , t ≥

A: Given,            ut-u=uxx;    0≤x≤π2, t≥0           ...(1)Boundary conditions                 ux(0,…

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Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the initial value problem y y" +2y-8y = 9 Cosx-2 sinx yea) = 4, y co) = -6

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