. a . Calculate L^-1 (1)/(s^3)-7s^2+10s)

Question

Answer 1

To calculate the inverse Laplace transform of

, we can use partial fraction decomposition.First, let's factor the denominator:

Now, we can decompose the fraction into partial fractions:

Multiplying both sides by the common denominator

, we get:

Expanding and simplifying, we have:

Combining like terms, we get:

Comparing coefficients, we have the following system of equations:

Solving this system, we find:

Now, we can rewrite the original expression as:

Taking the inverse Laplace transform of each term separately, we get:

Therefore, the inverse Laplace transform of

is:

Soru