1. ## laplace

Hi Guys,
Could you give my work a quick check... I'm hoping im doing this correctly :0

Find the solution to the following IVP using Laplace transforms:

y' + 3y = 2e^-4t with y(0) = 2

First, take the Laplace transform of both sides:

L[y'+3y] = L[2e^-4t]

sL{y} - y(0) + 3L{y} = 2/(s+4)

L{y} (s + 3) = 2/(s+4) + 2

taking the inverse laplace transform of both sides.

2/(s+3)(s+4) = A/(s+3) + B/(s+4)

A(s+4) + B(s+3) = 2

s=-4 s=-3
-B = 2 A = 1

Therefore, our transform equation becomes:

Taking the inverse laplace transform of both sides, we get:

2. Originally Posted by boousaf
Hi Guys,
Could you give my work a quick check... I'm hoping im doing this correctly :0

Find the solution to the following IVP using Laplace transforms:

y' + 3y = 2e^-4t with y(0) = 2

First, take the Laplace transform of both sides:

L[y'+3y] = L[2e^-4t]

sL{y} - y(0) + 3L{y} = 2/(s+4)

L{y} (s + 3) = 2/(s+4) + 2

taking the inverse laplace transform of both sides.

2/(s+3)(s+4) = A/(s+3) + B/(s+4)

A(s+4) + B(s+3) = 2

s=-4 s=-3
-B = 2 A = 1

Therefore, our transform equation becomes:

Taking the inverse laplace transform of both sides, we get:

Your answer is correct. Remember you can always check your work by taking derivatives and pluggin into the equation.

3. You are indeed correct! Well done!

4. thanks guys, very much appreciated!