Let Dy 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.) D) = 2x + 4

Q: Let z = x3 y2 ,x=t3, y=t+3 Use the chain rule to find dz at t=3 dt

A: By chain rule of partial derivatives,     dzdt=∂z∂xdxdt+∂z∂ydydt Here we have,       z=x3y2,   x=t3…

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: y" – 3y' + 2y = e3t ; y(0) = y'(0) = 0

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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: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: Use the Laplace transform to solve the initial value problem y''+y'−2y=2e3t,y(0)=−1,y'(0)=4 y(t)=

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Q: In each exercise, obtain the general solution. 1. dr/dt = -4rt; when t = 0, r = rg. 2. xyy' = 1+ y²;…

A: We solve these differential equations by separation of variables.

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te", y(0)=4, y'(0) = 2

A: The given question is related with Laplace transform. Given that,                    y'' - 4y' + 4y…

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te²", y(0)=4, y'(0)=2 %3D

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

Q: Use the Laplace transform to solve the initial value problem y" + 2y' + y = 4e-t; y(0) = 9, y'(0) =…

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Q: Verify that the given functions are linearly independent by evaluating the Wronskian at x = = 0.…

A: Given a set of functions e2x ,  xe2x , cosx , sinx . To verify that the functions are linearly…

Q: Suppose  y =    2x + 1,  where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x =…

A: Ans- (a)=30, (b)=1 .....detailed solution I have done ...hope you will get it easily...thanks

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: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: Use the Laplace transform to solve the given initial value problem y" – 4y' + 4y=r'e", y(0)=0,…

A: Given- y" - 4y' + 4y  =  t3 e2t Where,  y(0) = 0 y' (0) = 0

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: use an appropriate graphing device to draw the direction field and sketch the trajectories…

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Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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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: 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: 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 given initial-value problem. y' + 5y = e4t, y(0) = 2 %3D y(t)…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

A: The given differential equation is; 2y'''+3y''-3y'-2y=e-t,y(0)=0,y'(0)=0,y''(0)=1.

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

A: A)  6

Q: Use the method of Laplace transforms to solve d2f/dt2 + 2 df/dt + 5f = 0, f(0) = 1, f'(0) = 0

A: NOTE: Refresh your page if you can't see any equations. . for simplicity use the variable 'y' for…

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: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Compute the derivative: d I/ In(t° + 1) dt dx

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Q: Use the Laplace Transform to solve the initial value problem. y" -6y + 13y 0, y(0) = 0, y ((

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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: y' + v = e2t y(0) = 0

A: Given the IVP y'+y=e2t....(1) with the initial condition: y0=0...(2) We shall solve the differential…

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

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Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

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: E. Find the orthogonal trajectories to the curve y = ax²- acx (s held fixed. %3D where a

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Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 2y' + y = 8(t – 3), y(0) =…

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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: 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: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

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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: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

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

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Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: Use the Laplace transform to solve the given initial value problem for y" – 6y – 16y = 0; y(0) = 8,…

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Q: Use Laplace transform to solve the ivp: dy/dt = -y +u1(t)(t-1); y(0) =2

A: Use Laplace transform to solve the ivp: dy/dt = -y +u1(t)(t-1); y(0) =2