Laplace Transformation Formulas
1
1. L[1] =
𝑠
𝑛!
2. L[t] =
𝑠^𝑛+1
1
3. L[eαt] =
𝑠−𝛼
-αt 1
4. L[e ] =
𝑠+𝛼
𝛽
5. L[sinβt] =
𝑠^2+ 𝛽^2
𝑠
6. L[cosβt] =
𝑠^2+ 𝛽^2
Laplace Differential equation Transformation
1. L[Dx] = sx(t) – x(0)
2. L[D2x] = s2x(t) – sx(0) – x’(0)
3. L[D3x] = s3x(t) – s2x(0) – sx’(0) – x’’(0)
4. L[D4x] = s4x(t) – s4x(0) – s2x’(0) – sx’’(0) – x’’’(0)
5. L[D5x] = s5x(t) – s4x(0) – s3x’(0) – s2x’’(0) – sx’’’(0) – x’’’’(0)
1
1. L[1] =
𝑠
𝑛!
2. L[t] =
𝑠^𝑛+1
1
3. L[eαt] =
𝑠−𝛼
-αt 1
4. L[e ] =
𝑠+𝛼
𝛽
5. L[sinβt] =
𝑠^2+ 𝛽^2
𝑠
6. L[cosβt] =
𝑠^2+ 𝛽^2
Laplace Differential equation Transformation
1. L[Dx] = sx(t) – x(0)
2. L[D2x] = s2x(t) – sx(0) – x’(0)
3. L[D3x] = s3x(t) – s2x(0) – sx’(0) – x’’(0)
4. L[D4x] = s4x(t) – s4x(0) – s2x’(0) – sx’’(0) – x’’’(0)
5. L[D5x] = s5x(t) – s4x(0) – s3x’(0) – s2x’’(0) – sx’’’(0) – x’’’’(0)
