A: Find the solution of the following differential equation by Laplace transform with initial conditions for each equation: dy (t) Sóy (t)dt F(0) = i- %3D dt

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A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

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A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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A: "Since you have asked multiple questions, according to our guidelines we will solve only the first…

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Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

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Q: Determine whether S is a basis for the indicated vector space. s = {(0, 0, 0), (2, 3, 5), (5, 4, 2)}…

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Q: Please solve the given non homogeneous heat equation ut(x,t) = uxx(x,t) − x u(0,t) = 0 u(1,t) = 0…

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Q: Determine the vector field of F. F(x, y) 3D yi — хј

A: Let us make a table to draw the vector field as shown in the image below.

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Q: Consider the following nonhomogeneous system. dx dy - 5x + 9y + 5, dt = -x+ 11y + 15 dt Find the…

A: To find: General solution of the system of Non-homogeneous differential equation: dxdt=5x+9y+5,…