Question

Use the Laplace transform to solve the linear constant coefficient differential equation

dt²/d²y+4dy/dt+6y(t)=2H(t) where H(t)
denotes the Heaviside step function, with initial conditions
y(0)=0y′(0)= dy/dt∣∣t=0=−1
[Hint: you will need the shift theorem again, and will get both sin and cos terms.]

Answer 1

To solve the given differential equation using Laplace transform, follow these steps: apply the Laplace transform, use the shift theorem, and take the inverse Laplace transform.

Step-by-step explanation:

To solve the given differential equation using Laplace transform, we'll follow these steps:

1. Apply the Laplace transform to both sides of the equation.
2. Use the shift theorem to simplify the transformed equation.
3. Take the inverse Laplace transform to find the solution.

By applying these steps, we can find the solution to the given differential equation.