solve the inital value problem ?′′ + 6?′ + 9? = 2?^(-t) ; ?(0) =4, ?’(0)...

solve the inital value problem ?′′ + 6?′ + 9? = 2?^(-t) ; ?(0) =4, ?’(0) = −6

Expert Solution

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Colby Messinger answered 1 year ago

1. Use the Laplace transform to solve the initial value problem. ?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0 2. Use...

1. Use the Laplace transform to solve the initial value problem. ?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0 2. Use the Laplace transform to solve the initial value problem. ?"+4?=?(?), ?(0)=1, ?′(0)=−1 = { 1, ? < 1 where ?(?) = {0, ? > 1.

Use the Laplace transform to solve the following initial value problem: ?″+6?′+58?=?(?−4) ?(0)=0,?′(0)=0 (Notation: write u(t-c)...

Use the Laplace transform to solve the following initial value problem: ?″+6?′+58?=?(?−4) ?(0)=0,?′(0)=0 (Notation: write u(t-c) for the Heaviside step function ??(?)uc(t) with step at ?=?t=c.)

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1...

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1 , x'(0)=0

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2...

Solve the initial value problem: Y''-4y'+4y=f(t) y(0)=-2, y'(0)=1 where f(t) { t if 0<=t<3 , t+2 if t>=3 }

Solve the given initial-value problem. X' = 2 4 −1 6 X, X(0) = −1 8...

Solve the given initial-value problem. X' = 2 4 −1 6 X, X(0) = −1 8 X(t) =

Solve the following initial value problem over the interval from t = 0 to 2 where...

Solve the following initial value problem over the interval from t = 0 to 2 where y(0) = 1 using the following methods. dy/dt=y*t^2−1.1y a) Analytical method b) Euler's method with h=0.5 at t=2 c) Euler's method with h=0.25 at t=2 d) Midpoint method with h=0.5 at t=2 e) Fourth-order Runge-Kutta method with h=0.5 at t=2 f) Display all yor results obtained above on the same graph

2. Use the Laplace transform to solve the initial value problem. ?"+4?=?(?), ?(0)=1, ?′(0)=−1 = {...

2. Use the Laplace transform to solve the initial value problem. ?"+4?=?(?), ?(0)=1, ?′(0)=−1 = { 1, ? < 1 where ?(?) = {0, ? > 1.

Solve the laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1

y(4)+18y''+81y=0 y(0)=2, y'(0)=8, y''(0)=0, y'''(0)=−108 Note; y(4) is the 4th derivative of y Solve the initial value problem y(t)=...

y(4)+18y''+81y=0 y(0)=2, y'(0)=8, y''(0)=0, y'''(0)=−108 Note; y(4) is the 4th derivative of y Solve the initial value problem y(t)= ?

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0)...

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0) = 0, y'(0) = 0, y''(0) = 0.

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