1. Solve the following differential equation: XY' - 2Y = x² 2. Solve the following partial differential equation: ac/at = Da²c/ax² 3. Find the laplace transformation for the followings: 1) A) X² ex B) X sin 3X 4. A hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T. 5. Solve the following differential equation using Laplace transformation; y(0) 3 & y(0) -6 0.25y+y-4=0,

Q: Use perturbation method to linearize the following nonlinear differential equation: Ý = Xsinê —…

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Q: list the elements of the subgroup generated by the subset {18, 24, 39} of Z

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Q: S e-t cos(e-t)dt 3.

A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

Q: Faster please

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Q: dy +y cot x = cos .x dx dy = xe* – 3y dx dy 1 = 2 x+1 -y |y(1) =1 dx

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Q: 2. a) Using Laplace transforms, solve the following first order ordinary differential equation y –…

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Q: dy (h) cot x=x+y dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Find the differential dy for each of the following: A. y= x - 2x + 1 +e* B. y=- 2)

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A: Given that, The rate of change at which the vertical position of an object moving in a…

Q: In Exercises 3-6, the vector X is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate…

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Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y = 2x – y…

A: We need to solve the D.E.

Q: у" — 5у" + 7у' — Зу %3D 20 sin(t) , У (0) — у'(0) — 0, у"(0) %3D —2

A: Consider the provided question, We have the find the solution of the given D.E by using the Laplace…

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A: Given that z''(x)+kmz(t)=0 Take ddx=D D2+km=0D2=-kmD=ikm

Q: Solve the following differential equation using Laplace transformation: d²y -8+ 23y = 4e-4; Subject…

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Q: E = 115,000ejo M = cosh (0.05 + j0.5) A = 400[cos(5)– jsin(5)] T = VM² – 1 200,000,000ejo.241 H %3D…

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Q: E = 115,000ejo M = cosh (0.05 + j0.5) A = 400[cos(5) - jsin(5)] T = VM² –1 200,000,000ej0.241 H = ЗЕ…

A: Given that E=115,000ej0, M=cosh0.05+j0.5, A=400cos5-jsin5T=M2-1 and H=200,000,000ej0.2413E We have…

Q: The differential equation (cos(x) sin(x) - xy²) dx + (y - x²y) dy = 0 can be solved by: B. exact…

A: Explained below

Q: 94 A) Solve the following differential equation using Laplace transformation: d²y +4y= 16t .y(0) = 3…

A: Q4. A) Solve the following differential equation using Laplace transformation:,        and .

Q: et A 2 and U = . Then A2017U is equal to

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Q: A classical equation of mathematics is Laplace's equation, which arises in both theory and…

A: The given function is; u=e6x cos(-6y)

Q: 1- Solve the following differential equation by using Laplace transformation: ỹ + 2y = 3et where…

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