Question

In: Advanced Math

Solve listed initial value problems by using the Laplace Transform: 3.      yll + 4y = t −...

Solve listed initial value problems by using the Laplace Transform:

3.      yll + 4y = t 1,    y(0) = 1, yl(0) = 1

Solutions

Expert Solution

We will take the Laplace transform both sides of the given differential equation and then using that the Laplace transform of y(t) is Y(s), we have the Laplace transform of y" as s​​​​​​2​​​​​Y(s)-sy(0)-y'(0), putting these values in the the above equation and then using the rules, we will get the solution y(t) of the given initial value problem.  

The Step by step explanatory solution is provided below.


Related Solutions

Solve listed initial value problems by using the Laplace Transform: 6.       yll − 3yl − 4y =...
Solve listed initial value problems by using the Laplace Transform: 6.       yll − 3yl − 4y = 4t − 5,     y(0) = 2, yl(0) = 4
Use Laplace transform and inverse Laplace transform to solve the givien initial value problems (c) y′′...
Use Laplace transform and inverse Laplace transform to solve the givien initial value problems (c) y′′ −2y′ +2y=e−t, y(0)=0, y′(0)=1
Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) =...
Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) = cos(t), x(0) = 0, x'(0) = 1
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y''...
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y'' − 4y' + y = 0; y(0) = 1, y'(0) = 0, y''(0) = 0, y'''(0) = 1
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y''...
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y'' − 4y' + y = 0; y(0) = 1, y'(0) = 0, y''(0) = 0, y'''(0) = 1
Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t),...
Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t), x(0) = 1, x'(0) = 1
Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y =...
Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y = e^ −t ; y(0) = 0, y′ (0) = 0. (b) d2y/dt2+ y = t subject to the initial conditions y(0) = 0, y′ (0) = 2 (c) dy/dt + 2y = 4e 3t subject to the initial condition 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
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 the initial value problem below using the method of Laplace transforms. y'' - 4y' +...
Solve the initial value problem below using the method of Laplace transforms. y'' - 4y' + 8y = 5e^t y(0) = 1 y'(0) = 3
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT