(d) Use Fourier Sine transform to solve: a'u du əx² ay² 00; [u(0,y)=0, u(x,0)=f(x); (u(x,y) →0, as x² + y² →→∞. = 0, 2 Hence deduce that the solution reduces to u(x, y) = ² tan-'[(#). when f(x)=1. π

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A: Given a differential equation:initial conditions are:

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A:

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A: The truncation error is O∆x2 and the step size is -∆x

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A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

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A: Solve the given problem.

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: follow next step

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A: Given:

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A: We will be graphing the slope field of the given differential equation along with the interpretation…

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A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

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A: Solve for the equation for the derivative

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A: We will check where given function is differentiable and then we will find the derivative of…

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A: