Solve the following differential equation using Laplace Transforms. y'' + y' - 2y = -4 , y(0) = 0 , y'(0) = 0

Question.

Solve the following differential equation using Laplace Transforms.

y'' + y' - 2y = -4 , y(0) = 0 , y'(0) = 0

Solution:

Solve differential equation using Laplace Transforms. y'' - 6y' + 5y = te^t , y(0) = 2 , y'(0) = -1

Question.


Solve differential equation using Laplace Transforms.

y'' - 6y' + 5y = te^t , y(0) = 2 , y'(0) = -1

Solution:

Solve by using Laplace Transforms. y'''' - 9y = 0 , y(0) = 1, y'(0) = 0 , y''(0) = 0 , y'''(0) = 1

Question. Solve by using Laplace Transforms.
y'''' - 9y = 0 , y(0) = 1, y'(0) = 0 , y''(0) = 0 , y'''(0) = 1

Solution:

Find the Laplace Transform of f(t) = {cos t , 0 <= t <= Pi ; 0, t >= Pi} using definition of Laplace Transform.

Question.

Find the Laplace Transform of f(t) = {cos t , 0 <= t <= Pi ; 0, t >= Pi} using definition of Laplace Transform.

Solution:

Question.

Find the Laplace Transform L{f(t)} for the functions

f(t) = {t^2, 0<=t<=4 ; {2, t>4}

and

f(t) = {t^3 , 0<=t<=2 ; 1, t>2}

Solution:

Use the Laplace transform to solve the given initial value problem y'' - 2y' + 2y = e^(-t) , y(0)=0 , y'(0)=1

Question. Use the Laplace transform to solve the given initial value problem 
y'' - 2y' + 2y = e^(-t) , y(0)=0 , y'(0)=1

Solution:

Use the Laplace transform to solve the given initial value problem: y''+2y'+5y=0 , y(0) = 2 , y'(0) = -1

Question. Use the Laplace transform to solve the given initial value problem:
y''+2y'+5y=0 ,  y(0) = 2 , y'(0) = -1


 Solution:

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

x''+3y'+3y=0 , x''+3y=te^-t, x(0)=8 , x'(0)=2 , y(0)=0

Use Laplace transform to solve the system, with the given initial conditions. x''+3y'+3y=0 and x''+3y=te^-t x(0)=8 x'(0)=2 and y(0)=0

laplace transform of the piecewise function y' -3y = {3, 0<= t< 1; 0, 1<=t}, y(0) = 2

Find laplace transform of the piecewise function y' -3y = {3, 0<= t< 1; 0, 1<=t}, y(0) = 2

y'' +4y = {4, 0 <= t< 1; 0, 1 <= t} y(0) = 3 y'(0)= -2

find the inverse laplace transform of the piecewise differential equations y'' +4y = {4, 0 <= t< 1; 0, 1 <= t} y(0) = 3 y'(0)= -2

y''''-9y=0 , y(0)=1, y'(0)=0, y''(0)=0, y'''(0)=1

Use Laplace transform to solve the initial value problem y''''-9y=0 , y(0)=1, y'(0)=0, y''(0)=0, y'''(0)=1

y''-6y'+5y=te^t y(0)=2, y'(0)=-1

Solve for Y(s), the Laplace transform of the solution y(t) to the given initial value problem
y''-6y'+5y=te^t y(0)=2, y'(0)=-1

Differential Equation Laplace Transform (Dirac Delta Function)

Homogeneous Differential Equation using Laplace Transform

y'' - 3y' - 28y = 0 , y(0) = 5 , y'(0) = 7

Convolution Theorem (Laplace Transform)