Use Laplace transform to solve the following boundary value problem of heat equation du d²u di dx² u(x,0) = 0, du dx -(0,1)=0, u(L,0)= To, where To is a constant. 0 0, 0 0, t>0

Q: The doctor prescribes 25mg/kg divided into 3 equal doses for a todddler whom was 42 lbs. find the…

A: The weight of the child is 42 lbs The weight of the child in kilograms is 42×0.4536=19.0512≈19…

Q: dw Use the chain rule to find dt dw dt II W = In x² + y² + z² x = 7 sin(t), y = 4 cos(t), z = 3…

A: dtdw​=49sin2(t)+16cos2(t)+9tan2(t)33sin(t)cos(t)+9tan(t)sec2(t)​ Note: it can be simplified in many…

Q: (b) x' + 2y' + x = 0, x' − y' + y = 0, x(0) = 0, y(0) = 0 -

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Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: Ise the "mixed partials" check to see if the following ct find a function F(x, y) whose…

A: Introduction: Assuming that functions P(x,y) and Q(x,y) have continuous partial derivatives in a…

Q: dx Q1/ By Laplace transforms, solve the equation 3 dt - 4x = sin2t given that at t=0, x= 3

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Q: Solve using Laplace transforms. y" – y' + 5y = 58(t –"/6) sin t y(0) = y'(0) = 0 -

A: The Laplace transform is an integral transform that converts a function of a real variable t to a…

Q: B. If R = xyz’i+÷j – yz*k_find of the differential R, dR.

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Q: ) Apply the Laplace transform to the initial value problem and solve for Y(s) = L {y} (s) %3D y" +…

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Q: Use Laplace of derivatives to solve the F(s) and compare the result when using the Laplace Table.…

A: Laplace transform of a function f is denoted by L[f(t)] which is defined as  Lf(t)=F(s) =∫0∞f(t)…

Q: dz If z = f(x, y) = x² + 2xy² and (x(t), y(t)) = (cos 2t, 2 sin t), use the Chain Rule to find…

A: We have to use the chain rule for finding the required derivative

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: Function u(x,t) at an interval is given by the partial differential equation u = u, – 3u , 00. %3D…

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Q: Solve using Laplace Transforms y" +y = f(t) y(0)=1, y'(0)=0 %3D f(t) = (sin ce) 1 0 T/2 ) %3D

A: According to the given information, it is required to solve the equation using Laplace transforms.

Q: Use the Laplace transform to solve for the given initial value problem. y' – 2y = 1 - t y(0) = 4 y"…

A: We will use the following Laplace formulas to solve IVPs

Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

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Q: dy Find if y is a function of x defined dx implicitly by xy? + cos(yx) = e*y + In x

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Q: 3) Solve using Laplace Transforms: y"+y = 6 u(t – 3), y(0) = 1, y'(0) = 0

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