Let 7(t) 3 t – 2, et ). Evaluate the definite - t - integral. 3 F(t)dt = ( 2.

Q: Use Laplace transforms to solve the initial-value problem j – 9y = f(t), y(0) = 2, ý(0) = 0, where…

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Q: Solve the solution of the DE of the Gompertz function: dP = c In[P dt М In[P

A: We have a nonlinear ordinary differential equation :

Q: Find an integral representation for a general solution of the differential equation d'y dy dt +4 +…

A: Apply the method of variation of parameters, to find the particular solution of the second order…

Q: Use Laplace transform to solve the partial differential equation: o'y dy +xt where y(x,0)= 0,…

A: Solution

Q: use Laplace Transform to solve the following differential equation d²y(t) + 6) + 8y(1) = u(1). (0) =…

A: differential equation:d2ytdt2+6dytdt+8yt=ut; y0=0, y'0=1We have to solve the differential equation…

Q: Use Laplace transform to solve the partial differential equation: d²u d²u du(x,0) = t> 0, 0<x<1,…

A: Solution

Q: -2-3 Evaluate the integral o S Jy² 2y dx dy.

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Q: 3 Suppose g(t) dt = 23. Calculate the following integrals: 6. (a) dt 3 (b) g(3 – t) dt = %3D

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Q: Use Laplace transforms to solve the initial value problem x'=x+2y, y'=x+e^-t; x(0)=y(0)=0

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Q: Just use the definition L{f (t)} = ° e-st f (t) dt with 2 integrals, one for 0 1

A: Laplace transferom

Q: Use the Laplace transform to solve the given initial-value problem. dy — у %3D 1, у(0) %3D 0 dt

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Q: Verify the initial value theorem of f(t) = 1 +e¯t[sint + cos os t]. 3 1 0 2

A: Solution :- As per guidelines I solve only first question .

Q: Use Laplace transform to solve the initial-value problem,y′′+4y=1−u(t−1); y(0)=0,y′(0)=−1

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Q: 1-t2 is 1+t2 The differential of u= In,

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Use Laplace transform to solve the partial differential equation: d²u du du(x,0) = , t> 0, 0<x<1,…

A: Solution

Q: Verify the initial value theorem of f(t) = 3 + 4 cos 2t. 7

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: If s(0) dt: 20z 4, then f (t) dt is -3 E) divergent

A: A)  6

Q: Use the Laplace transform to solve the given system of differential e dx 4x + d³y dt3 = 12 sin(t) dt…

A: dxdt−4x+d3ydt3=12sintdxdt+2x−2d3ydt3=0x0=0, y0=0, y'0=0, y''0=0

Q: Use laplace transform to solve the given system of differential equation; a) {dx/dt=2y+e^t…

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Q: Use the Laplace transforms to solve the differential equations: d²y dy 1.)- +6 +13y = 0, given that…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Consider the following. dt 49 + t2 Let t = 7 tan(0) and determine the following. dt = de t = 0 - 0 =…

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) take derivative…

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u(x) =1-x - (x -t u (1…

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Q: Use Laplace transform to solve the partial differential equation: ²ud²u du(x,0) t> 0, 0<x<1, u(x,0)…

A: Solution :-

Q: Use the Laplace transform to solve the given system of differential equations. dx = -x + y dt dy =…

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Q: Use the Laplace transform to solve the given system of differential equations. dx = 3y + et dt dy =…

A: We have given two equations dxdt=3y+et                ...(1) dydt=12x-t                ...(2) The…

Q: dx Integrate: J. 3n B. A. EIN

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Q: х-2 Evaluate the integral S (t3 In ti+ 3t3 sin (t*) j+ k) dt. x(x+1)

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Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt Jo 2-

A: Given :  Two inetrgal parts with finite limits which we have to solve

Q: Let g be continuous on [a, b), and let f(x) = S (x – t)g(t) dt. Prove that f is a solution of the…

A: Given that g be continuous on a, b and let f(x)=∫ax(x-a)g(t)dt. And we have to show that f is a…

Q: The expanded form of the differential operator D(xD - 1) is (A) XD²-1 (в XD²+1 XD² - D XD² D

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Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

Q: Consider the following initial-value problem for u(x, t), du du = Au XER", dt Əx1 |u(x, 0) = f(x),…

A: As per the question we are given a partial spatio-temporal differential equation in Rn dimensions,…

Q: The expanded form of the differential operator D(xD -1) is A xD +1 O xD? -D © xD? -1 (D) O xD?

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Q: Solve the Abel's integral equation: a dt = æ(1+x) y(t) (1-t)1/3

A: Given integral equation, ∫0xyt1-t13dt=x1+x

Q: Use the Laplace transform to solve the given system of differential equations. 2. dx = x - 2y dt dy…

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Q: Show that (D+ 3t)D , is not the same as D(D+3t), where D is the differential operator.

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Q: By the Fundamental Theorem of Calculus: •t „2 +1 dx 5x +1 d dt d and dt - 6t x2 +1 dx 5x +1 d…

A: Given

Q: Let g be continuous on [a, b), and let f(x) = S. (x – t)g(t) dt. Prove that ƒ is a solution of the…

A: The given differential equation is                                           f''=g…

Q: Use the Laplace transform to solve the given system of differential equations. dx dt dy = 5x - y dt…

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

A: Solution

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u (x ) = 1-x - (x –t )u…

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Q: 2. Evaluate the given integral without change of variable. t3 + 1 dt VE (t + 1)

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Q: Solve the ODE dy/dt = -2y between t = 0..4, with the initial condition y(t=0) = 1.

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Q: 79. Evaluate the integrals. dt dt b. a. Vi(1 + t) Vi(1 + t)

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Q: The expanded form of the differential operator D(xD – 1) is A XD2 B xD2 - D © xD² +1 D xD² - 1

A: Given that: D(xD-1) find expand form of the differential operator . And again given that :(D3 -5D2…

Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: Use the Laplace transform to solve the given system of differential equations. dx/dt = -x+y dy/dt…

A: Given: A 0.25 kg object with the speed of 6 m/s at point A and kinetic energy of 8 J at point B.

Q: Consider the following. dt (4 + t? Let t = 2 tan(0) and determine the following. 2 sec-(0) dt = de t…

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Q: Solve the following differential equation using the Laplace transform dy 4- dt + 6y = 3t if t = 0…

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Q: Use the Laplace transform to solve the following system of differential equations. dx = x - 2y dt dy…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.