Question

Write the partial fraction decomposition of

s³+9s-3s²-24/s(s-3)(s²+9)
​Find the general solution to x '′ −3x' =sin3t;x(0)=1,x' (0)=0, Using any method

Answer 1

To find the partial fraction decomposition of the given expression, we first factor the denominator and then equate coefficients to solve for the unknowns.

Step-by-step explanation:

To find the partial fraction decomposition of the given expression, we first factor the denominator:

`s^3 + 9s - 3s^2 - 24 = s(s-3)(s^2+9)`

Next, we write the expression with unknown coefficients:

`s^3 + 9s - 3s^2 - 24 = (A)/(s) + (B)/(s-3) + (Cs+D)/(s^2+9)`

Combining the fractions and equating coefficients, we can solve for A, B, C, and D.