using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = -...

using the Laplace transform solve the IVP

y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the partial fraction decomposition step. please explain the decomposition clearly.

Expert Solution

Colby Messinger answered 1 year ago

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

Solve using the Laplace transform: y" + 4y = g(t) where y(0) = y'(0). Hint: Use...

Solve using the Laplace transform: y" + 4y = g(t) where y(0) = y'(0). Hint: Use the convolution theorem to write your answer. You may leave your answer expressed in terms of an integral.

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use laplace transform to solve the initial value problem: y''+4y=3sint y(0)=1, y'(0)=-1

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t...

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t y(0)=0,y′(0)=0 Y(s)= ? Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t). Use step(t-c) for the Heaviside function u(t−c) . y(t)= ?

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

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Again considering y'' + 4y' + 3y = 0: (a) Solve the IVP y'' + 4y'...

Again considering y'' + 4y' + 3y = 0: (a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where α > 0. (b) Determine the coordinates (tm,ym) of the maximum point of the solution as a function of α. (c) Determine the behavior of tm and ym as α →∞.

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