Question

solve y''+5y'+6y=2 where y(0)=y'(0)=0 using laplace transformation.

Answer 1

Start by taking the Laplace transforms of both sides, using linearity.

Let \[Y(s) = \mathcal{L}[y(t)]\] \(\mathcal{L}[y'']+5\mathcal{L}[y']+6\mathcal{L}[y]=\mathcal{L}[2]\)

Now use your laplace table see if you can set it up, look down at 35 - 37

Answer 2

So what I mean is \[\mathcal L [f''(t)] = s^2 Y(s)-s f(0)-f'(0)\] etc