Question 7. Use Fourier transform to solve the following problem: ut = 2uxx - 5и, -∞ < x <∞, t > 0, -3|x| u(x,0) = e-³x, е lim u(x, t) = 0, x →∞ where u(x, t) represents the temperature of an infinite rod whose sides are not insulated.

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A: Please see the attachment

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Q: Q6: Find the outward flux generated by the field F=zk across the hemisphere x² + y² + z² = 3, z20.…

A: We have to find the flux across the hemisphere  x2+y2+z2=3Generated by the vector field F= zk

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Q: ① Solveing dy - - x dx = 。 ㅎ

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Q: 8) Let a 3-2 +45 for n-0, 1, 2, 3, ... If we write an as a recursive relation, it is Hint: calculate…

A: Please see the attachment

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A: We have determined the inverse Laplace transform for ℒ-15s+2s2+6s+13 .

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Q: Find a solution to y" - 4y' - 5y = 2e²t using variation of parameters.

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