# Thread: more unit step functions...

1. ## more unit step functions...

ok im having a bit of a time solving this problem...

y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

the Unit step is giving me a problem...can i just make it e^-s and solve it?

any help would be appreciated..

2. Originally Posted by slapmaxwell1
ok im having a bit of a time solving this problem...

y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

the Unit step is giving me a problem...can i just make it e^-s and solve it?

any help would be appreciated..

Split the problem in two parts...

a) find the solution of the initial values problem...

... and call $\displaystyle \varphi$ this solution...

b) find the solution of the initial values problem...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Originally Posted by slapmaxwell1
ok im having a bit of a time solving this problem...

y''-5y'+6y=U(t-1) y(0)=0, y'(0)=1

the Unit step is giving me a problem...can i just make it e^-s and solve it?

any help would be appreciated..

$\displaystyle \mathcal{L} \{ U(t - t_0) \} = \frac{e^{-st_0}}{s}$
Since $\displaystyle t_0 = -1$ what is the sign in the exponential?