4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, ut = a²uxx- uz (0, t) = -(10e-0.1t) ift 20 ift 20 if 0 ≤ x ≤ 1 (c) u₂(1, t) = 0 u(,0) = 0

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A: We have to solve the given problem using Laplace transform method.

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A: We can solve this problem by Laplace transforms.

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

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A: I have to solve differential equations in this question.

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A: initial/ boundary conditions, U(x, 0)= f(x), u(0, t)= 0, u(L, t)=0

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A: Given IVP is  y"-y= 4cos(t).....(1) y(0)=0,y'(0)=1....(2) We solve this initial value problem by…

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A: Since there are many sums, therefore find here the solution of part (a).

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

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