Laplace Transform : y ' - y = e^-3t cos3t , y(0) =3 and, Show that,...

Laplace Transform : y ' - y = e^-3t cos3t , y(0) =3

and, Show that, Differential Form ?

dU = Tds - Pdv , dH=Tds-Vdp , dF= -sdT-Pdv , dG= -sdT+VdP

Expert Solution

milcah answered 1 year ago

Solve using laplace transform y" + 3y = -48t^2e^3t ; y(0) = 2 , y(0) =...

Solve using laplace transform y" + 3y = -48t^2e^3t ; y(0) = 2 , y(0) = 1 y" + 6y' + 5y = t - tu(t-2); y(0) = 1 , y'(0) = 0

y''-3y+2y=e^3t y(0)=1 y'(0)=0 laplace transformation

Use the Laplace transform to solve the following initial value problem: x′=12x+3y y′=−9x+e^(3t) x(0)=0, y(0)=0 Let...

Use the Laplace transform to solve the following initial value problem: x′=12x+3y y′=−9x+e^(3t) x(0)=0, y(0)=0 Let X(s)=L{x(t)}, and Y(s)=L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): X(s)= Y(s)= Find the partial fraction decomposition of X(s)X(s) and Y(s)Y(s) and their inverse Laplace transforms to find the solution of the system of DEs: x(t) y(t)

solve using the laplace transform y''-2y'+y=e^-1 , y(0)=0 , y'(0)=1

Solve with Laplace transform 1. y''+ 4 t y'− 4y = 0, y(0) = 0, y'(0)...

Solve with Laplace transform 1. y''+ 4 t y'− 4y = 0, y(0) = 0, y'(0) = −7 2. (1− t) y''+ t y' − y = 0, y(0) = 3, y'(0) = −1

Apply the Laplace Transform to solve the initial value problems 1. y' + 2y = 2cos(3t)...

Apply the Laplace Transform to solve the initial value problems 1. y' + 2y = 2cos(3t) , y(0) = 1 2. y'' - 3y' + 2y = 2 - 10e-3t , y(0) = -1 , y'(0)= 1

Give the Laplace transform of the solution to y"+2y'+3y=0 y(0)=-5 y'(0)=4

Use a Laplace transform to solve the initial value problem: y''' =y+1, y(0) = 0, y'(0)...

Use a Laplace transform to solve the initial value problem: y''' =y+1, y(0) = 0, y'(0) = 0, y''(0) = 0.

a) do the laplace transform to; x(t)= e^2t . sin(3t) . sin (t) b) do the...

a) do the laplace transform to; x(t)= e^2t . sin(3t) . sin (t) b) do the inverse laplace transform to; x(s) = (3s-5) / ( (s+1).(s^2+2s+5) )

solve the d.e. equation using Laplace inverse transform y'-y = xex, y(0)=0

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