Take the Laplace transform of the IVP Use Y for the Laplace transform of y. (not Y(s)). So d²y dt² +k²y=et,y(0) = 0, '(0) = 0

Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

A:

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

A:

Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

A:

Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

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: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

A:

Q: Find the Inverse Laplace Transform of the following: 2. Y(s) = /(2s– 3)5

A:

Q: y" + y' = t; y(0) = 1 , y'(0) = -2

A:

Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

A:

Q: So (sinh (-2t)e¯') u(t)

A: We shall find the Laplace transform of∫0tsinh-2te-tutdt that is L∫0tsinh-2te-tutdt First Shifting…

Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

A:

Q: Solve the shifted data IVP by the Laplace transform method showing your work in details.…

A:

Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: y""-4y" +5y'-2y = 7t-5, y(0) = 0, y'(0) = 0, y"(0) = -2

A:

Q: Please help me find the laplace transform of the following equation: 0.00174y''+0.295y'+25y=200u(t)…

A: If Ys is Laplace transform of yt. Then Laplace transform of y' and y'' when y(0)=0, y'(0)=0 is sYs…

Q: Solve the following ODE 3t. y" – 6y' + 9y = t²et; y(0) = 0, y'(0) = %3D

A: Given The given ODE is y"-6y'+9y=t2e3t. y0=0,    y'0=1 Apply formula…

Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

A:

Q: Find the Laplace Transform A- f)=tcos(@r) B- f(1)=tsin(@t) C- f(t)=tcosh(at)

A:

Q: Determine the Laplace transform of the function. a) [4+sin(31)+5e²]- b) Z[6r'+2t’e" +sinh(4)].

A:

Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint A) 1- e-t t-e-t O

A:

Q: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

A: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…

Q: у" + 2y'— Зу%3D бе 3t У (0) — 0, у' (0) - 0 %3D

A: Here we use simple Laplace transform to solve this

Q: sin at Find the Laplace transform of f(1) = ·S' dt 0 1

A: To find the Laplace transform of ft=∫0tsinattdt The Laplace transform of sinat is ℒsinat=as2+a2 The…