Question

Solve the following differential equations using Laplace transform method.

(a) y˙​(t)+y(t)=2et, y(0)=4 Ans: y(t)=et+3e−t
My Question Ans. (a) Taking Laplace transform,
sY (s) - y(0) + Y(s) = 2 (1/s-1)

How to take the Laplace transform?

Answer 1

To take the Laplace transform of a function, follow these steps: apply the initial condition, take the Laplace transform of both sides of the equation, solve for Y(s), and invert the Laplace transform of Y(s) to find y(t).

Step-by-step explanation:

To take the Laplace transform of a function, you can follow these steps:

1. Apply the initial condition: y(0) = 4. This is the starting condition for the equation.
2. Take the Laplace transform of both sides of the equation: sY(s) - y(0) + Y(s) = 2 / (s-1), where Y(s) represents the Laplace transform of y(t).
3. Solve for Y(s): sY(s) - 4 + Y(s) = 2 / (s-1). Combine like terms to get (s+1)Y(s) = 2 / (s-1) + 4. Simplify and rearrange the equation.
4. Invert the Laplace transform of Y(s) to find y(t):
   `y(t) = e^t + 3e^(-t).`This is the solution to the given differential equation.