(a) Show that V(x, t) = π - fx es² ds is a solution to the heat equation √4xt Vt=xVxx, xER.

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Q: 3 Solve the differential equation 3x²y" + 11xy¹ - 3y = 8-3. lnx

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Q: 09 10 11 Problem: Find the solution of the following equation. 2 Judu + 2 du_y² ду au и u (X₂6) = 2x

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Q: infinty use L.23 and L32 of Laplace Transform Table to evaluate Ţ [t] (2t). dt. 0

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Q: ∞ if y ‡ 0 and yn #0 for all n € N, then (2) 1 converges to Yn n=1 ৪১১

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Q: ind two series solutions of the differential equation: x²y" + xy' + x²y = 0.

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Q: 4.4-3. Consider the following problem. Z = 2x₁ + x2, Maximize subject to x₁ + x₂ ≤ 40 4x₁ + x₂ = 100…

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Q: Determine whether each of the following series are convergent or divergent. i. ∑ cos2 n / (n2 - 3)

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Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t I U(x, 0) = 0.

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Q: Expand the function f(x) = x sinx, as a Fourier series in the interval - < x < π.

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Q: 2 JO) = {0 -2t 21 0 H.W 1) Find the Laplace transform of f(t) shown in Fig. 08 2 01 -2 0 Slope=2 1…

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Q: thank you

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