Is my unit step function correct for solving this differential equation?

[gbuitkus]

Homework Statement

y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t
y(0)=y'(0)=0

Homework Equations

The Attempt at a Solution

s²L(y) -4sL(y)-32 L(y)=u₁(t)

I am just struggling to figure out if my unit step function is correct.

Solving for L(y) I get:
(e^-s) / (s(s² -4s-32))
but it says I am wrong so I am pretty sure I am doing something wrong with the unit step function

 

[LCKurtz]

Homework Statement

y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t
y(0)=y'(0)=0

Homework Equations

The Attempt at a Solution

s²L(y) -4sL(y)-32 L(y)=u₁(t)

I am just struggling to figure out if my unit step function is correct.

Solving for L(y) I get:
(e^-s) / (s(s² -4s-32))
but it says I am wrong so I am pretty sure I am doing something wrong with the unit step function

You didn't explain what your notation $u_1(t)$ means. Is it $u(t-1)$? What you want on the right side is $u(t)-u(t-1)$.