The discussion centers on solving the differential equation y'' - 4y' - 32y = {1 when 0 <= t < 1 and 0 when t >= 1} with initial conditions y(0) = y'(0) = 0. The user is attempting to apply the Laplace transform but is uncertain about the correct formulation of the unit step function. The correct representation for the right-hand side should be u(t) - u(t-1), which accurately captures the piecewise nature of the function. The user's initial approach using u1(t) was incorrect, leading to confusion in the solution process.
PREREQUISITESStudents studying differential equations, particularly those learning about Laplace transforms and piecewise functions. This discussion is beneficial for anyone seeking to clarify the use of the unit step function in solving differential equations.
gbuitkus said:Homework Statement
y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t
y(0)=y'(0)=0Homework 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