Solve the following heat equation by means of the method of separation of variables: au ;0sxs a, tz 0 at u(0, t) = 0 (7, t) = 0 5x u(x,0) = 3 sin- 2

Q: Find '(t), given r(t) = (-4e-²t, 4t² + 3, 3 sin(−3t)). r' (t) =

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Q: Convert the following 2nd order IVP to a 1st order system IVP, by viewing y' as a second dependent…

A: Given: We have to convert the given 2nd order IVP to a 1st order system IVP, by viewing  as a second…

Q: H. JJ HY BY 4.6 where y(0)=0 y'co)=2

A: Given differential equation is y''+4y'+3y=4e-x with y(0)=0 and y'(0)=2We know the formula that PI of…

Q: Ut = Uxx e-3t sin(5x) + e−²t sin x, -2t u(0,t) = u(T,t) =0, u(x,0) = sin(2x).

A: Introduction: Laplace transformation and inverse Laplace transformation is very significant in…

Q: Solve the following equation: (X² + y²) dx = 8 (XY)dy, and find the value of y at x = 5 where y = 0…

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Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Find the solution of the IVP. y" + 3y' + 2y = 20 (sin t + 8 (t – 1)), y (0) = 1, y' (0) = –1

A: We solve the given initial value problem by using Laplace transform.

Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

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Q: find the general solution : 6- y' +4y = 4 sec 2x

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Q: can y' = sin(xy) be solved using separation of variables ? Select one: O a. l am not sure O b. Yes O…

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Q: (t + z cos(t)) dt + (sin(t) – 3z² + 5) dz = 0

A: Let's find.

Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: Given f(x, y, z)= 10 x y z-5, use the total differential to estimate the change in f from the point…

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Q: Find f. f"(0) = sin(0) + cos(0), f(0) = 1, f'(0) = 4 %3D %D

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Q: y" + 4y" +y' – 6y = 2e¬t + 5 cos t y" + 4y' = 16 sin 2t , y(0) = 2, y'(0) = -2, y"(0) = 4

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Q: b) d² y dx² +4y= cos 2x, y(0) = 2, y'(0) = 4

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Q: y" + 4y – 5y = –260 sin(5x).

A: To solve the given differential equation

Q: dw 4w A) Give the general solution of dx = x³. B) Solve y' + = y²x³.

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Q: 2 cos(2z)- V3 = 0.

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Q: Given f (x, y) = 5e¹2 sin (4y) then f (0.)-[ Vf = 2

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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: 5. Find (b) y = cos (11x + 5x).

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Q: 5. 2e* cot y dx - (4 + e*) csc²y dy = 0

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Q: y =V2 e-c is a solution of y' y sinx. -Cosx Select one: O True False

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Q: Use the d'Alembert solution to solve 1 0u 9 dx2' u(x, 0) = cos? x, u(x,0) = e"+1. -0 0, t > 0,

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Q: Find the general solution of the following homogeneous equation. dy/dx=y/x+x^2/y^3

A: I have explained everything within the solution. Please go through.

Q: Estimate the amount of change in f (x, y,z)= cos (7xy)+xz² if the point P(x,y,z) moves a distance of…

A: Given that f(x,y,z) = cos(πxy) + xz2 If the point (x,y,z) moves a distance of ds=0.1units from…

Q: Nitin

A: (a) y(t)= ±5.83 cos(3t-30.96o)(b) Time period of the motion = 2.09 s      Frequency of the motion =…

Q: Calculate the order of the local truncation error of the Crank-Nicolson method for approximating the…

A: We are given the heat equation as ∂u∂t-∂2u∂x2=0. Now, we will be approximating the heat equation by…