Use Laplace transforms to solve the following heat problem: U₁ = Urr x > 0, t> 0 u(x, 0) = 10c a -X u(0,t) = 0 lim u(x,t) = 0 I7X
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- Solve the IVPx”+9x = U(t-2)sin[3(t-2)], x(0)=2, x’(0)=0using Laplace Transforms. Identify xc, xpinyour solutions. Show work to justify youranswers.Apply the Laplace transform to the following differential equations, ie solve in the image area. Use the attached table for this:By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point (x, y, z) moves from (-1, –1, 4) towards (-4, 2, –6) a distance of 0.02?