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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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: Exercise 3.5 Determine a particular solution of the following 2x -Sy'+6y=e* 1.

A: As per guideline we have to solve only one question.We have to find the particular Integral

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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A: given differential equation :-             y''' + y' = 1

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Q: 2014. (₁) flts = filt = Are Length 2 = 0 X7, > 36s1u2+36 cas ² 6 + +9 3√5 dt ₂ 36 +9 = (+²+3) ²…

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Q: 3. Consider the periodic system y' = A(t)y, -1+ 0t 1-ost sin |-1- sint cost ) 3 cos2 2 3 3 A(t) = 2…

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

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