Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function. (Use C for the constant of integration.) DN = 2x +9

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: Use the Laplace transform to solve the initial value problem. (a) y" – y' – 6y = 2, y(0) = 1, y'(0)…

A: Laplace transform

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

A: please see the next step for solution

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: Use the Laplace transform to solve the given system of differential equations. 1. dx -x + y dt dy 2x…

A: According to question, Given differential equation, dxdt = -x+y,dydt = 2x,x0 = 0,y0 =1

Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

A:

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Use the Laplace transform to solve the initial-value problem, у" — Зу' + 2у — sin(t); y(0) %3 0, у'…

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Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: Use the method of Laplace transform to solve the initial value problem y" + B²y = (a² + ß²)et, y(0)…

A: The solution is given as

Q: find the differential of each function

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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: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: With the aid of Laplace transform, calculate the initial value of the equation below.…

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Q: Find the Laplace Transform of y in the differential equation (D2 + 5D + 3)y = 10 Assuming the…

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Q: Use the fundamental theorem of calculus and the chain rule to find (A(x)) where dx e2x A(x) = In(t?)…

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Q: Use the Laplace transform to solve the initial value problem. x' + 2y' - y = 1; 2x' +y = 0; x(0) =…

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: Use the Laplace transform to solve the initial value problem. y" – y' – 6y = 2, y(0) = 1, y'(0) = 0…

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Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: Use Laplace transform to solve the initial-value problem,y′′+y=3; y(0)=1,y′(0)=1

A:

Q: Use the Laplace transform to solve the given initial-value problem. y"+y= (t-극) + 이t-), y(0)= 0,…

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

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If x2 + y2 = 25, and dx = 2 when x = 3…

A: Given that x=x(t) and y=y(t) are both functions of t . If  x2+y2=25           ..(1) Differentiate…

Q: Use the Laplace transform to solve the given system of differential equations. dx/dt=x-2y dy/dt=5x-y…

A: The given system of differential equation are

Q: Use the Laplace transform to solve the initial value problem y" + 4y = e2t, y (0) = 1, y' (0) = -1.

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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: cos(x + y), when x = 0,y = dx

A: To solve the given first order differential equation using integration method. dydx=cos(x+y)  , when…

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

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Q: Find an integrating factor to obtain the integral curve of (2ау — 16х) da + dy 3 0 that pass -…

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Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

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Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Apply the appropriate integration techniques to evaluate 9x? dx S- а. b. fxsin dr. 2 c. f(2x – 8)°dx…

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Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: The Integrating Factor for the DE y dx = (ye' – 2x)dy %3D is: -2y レマ None of These 2y

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Q: Use the Laplace transform to solve the initial value problem below. y" – 2y' + ly = t, y(0) = 0 ,…

A: Given : differential equation              y''-2y'+y=t               --------- (1) with…

Q: Find the total differential of z = In (2x – 3y).

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Q: Find the Integration of: Ja (3sint + esin t) cost dt In 3 2

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Q: Use the Laplace transform to solve the given initial-value problem. dy - y = 1, y(0) = 0 dt y(t) =

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Q: evaluate (b) By repeated applications of the reduction formulae dx (HINT: First use integration by…

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Q: Solve the initial value problem using Laplace Transform: d²y dy + 5- dx + 6y = 0, y(0) = 0, y(0) = 1…

A: The solution is given as

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

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Q: dy + ydx %3D = 3x²y?dx,

A:

Q: If f(x, y) = 4x²y+7xy°, then the total differential of f at x = 1 and y = 1 is : %3D O df = 15 dx –…

A: Use formula of total differential

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

A: Consider the given differential equations and initial conditions,

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: Use the Laplace transform to solve the initial value problem. y''+ 36y = sin(6t), y(0) = 1, y'(0) =…

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Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z = xy3 - x2y, x = t2 + 1, y = t2 -1

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate:

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x