Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. y'' + 2y' - 8y = 6e^(-2x) - e^(-x)

Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0.

y'' + 2y' - 8y = 6e^-2x - e^-x

Laplace Transform Initial Value Problem y' + 4y = f(t), y(0) = 0, where f(t) = {t, 0 <= t < 1 0, t >= 1}

Use the Laplace transform to solve the given initial-value problem. y' + 4y = f(t), y(0) = 0, where f(t) = {t, 0 <= t < 1 0, t >= 1}

Inverse laplace transform e^- pi*s/(s^2+1)

Find Inverse laplace transform of e^- pi*s/(s^2+1)

2y''+3y'-2y=0, y(0)= - 1, y'(0)= - 3

Solve differential equation with initial value problem.

2y'' + 3y' - 2y = 0 ,   y(0) = - 1, y'(0) = - 3  

and find the limit as t approaches infinity

Laplace Transform y'' - 6y' +18y = 18 , y(0) = 0 , y'(0) = 3

Use the Laplace Transform to solve the following initial value problem.
y'' - 6y' +18y = 18 , y(0) = 0 , y'(0) = 3