Using Laplace to solve a differential equation

[sim907]

Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s²+3s+5)X(s)= 2s+3+ [8/(s²+64)] but stuck. Please help

 

[sim907]

Got it.

 

[MathWarrior]

Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s²+3s+5)X(s)= 2s+3+ [8/(s²+64)] but stuck. Please help

Try completing the square on (s²+3s+5)