6. (laplace transform) Given Y(t) + a²Y(t) = F(t) with the initial condition Y(0) = 1 and Y'(0) = -2. Determine y(s) = L{Y(t)}

Q: Let A(x) be the function defined by A(x) = 4 We have A(0) = -3 A'(-1/2) = -2 for x = [-1,0], A(x) =…

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Q: use the laplace transform to solve the initial value problem y''- 4y'- 4y = t^3          y(0) = 1,…

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Q: 3) Consider the function G(x) = f g (t) dt. Find the derivative G' (x). O g(x) g(x)-g(1) O g(t) O…

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Q: Evaluate the derivative (r1(t) × r2(t)) where r1(t) = and r2(t) =. (Use symbolic notation and…

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Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: SOLUTION -

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: 15) Let f(x) = f In (t² – 5)dt. Find f'(x) and then also find f"(x).

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Q: Find a function y(æ) such that byy' = x and y(6) = 5. y =

A: y' = dy/dx y(6) = 5 means at x=6 => y=5

Q: Find the Laplace transform F(s)=L{f(t)} of the function f(t)=e^(−3t) cosh⁡(5t).

A: Laplace transform of the function, f(t)=cosh(at) is

Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: y''+9y=10e-t,y(0)=0,y'(0)=0 by laplace transform

A: The objective of this question is to solve the given second order differential equation using…

Q: Find a function y(x) such that 5yy' = x and y(5) = 8. y =

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

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Q: Find y as a function of tif y(t) T y" + 16y + 80y = 0, y(0) = 5, y'(0) = 2.

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Q: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: 1. let y = x(x2+x)2  , Find y'   2. let f(x) = (5x)5 find f '(x)…

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

Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: A dilation T sends A = (2,3) to A’ = (5,4), and it sends B = (3,−1) to B’ = (7,−4). Where does it…

A: We have, A dilation T sends A = (2,3) to A’ = (5,4) and it sends B = (3,−1) to B’ = (7,−4) Where…

Q: y''+4y'+3y=sin(3t) with y(0)=1 and y'(0)=-1 determine with laplace transform

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Q: a) Using the definition of derivative, calculate the derivative of the function of f(x) = /3x +1 (b)…

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Q: 2. Let 1 f(x): Recall: L(x) = f(a) + f'(a)(x - a) and L(x) f(x) when x is close to a (a) Find the…

A: Given function is -  f(x) = 1/x

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: Laplave Transform

A: Solve the given differential equation by Laplace transform. The given equation is y''(x)+9y(x)=40ex…

Q: 4) Knowing that f = f(t), using the expressions of L[f'] and L[f"], derive an expression for d'f…

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Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: Find a function y(x) such that 3yy' = x and y(3) = 3. y =

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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