Use the Fourier transform to find the solution of the following
initial boundaryvalue Laplace equations
uxx + uyy = 0, −∞ < x < ∞ 0 < y < a,
u(x, 0) = f(x), u(x, a) = 0, −∞ < x < ∞
u(x, y) → 0 uniformlyiny as|x| → ∞.
Use the Laplace transform to find the solution of the IVP:
a.) 2y' + y = 1, y(0) = 2 (answer should be y(t) = 1 + e-t
/ 2 )
f.) 4y" + y = 0, y(0) = -1, y'(0) = -1 (answer should be y(t) =
-sin(t) - cos(t))
Please show work!
Consider the differential equation
y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,
A)Find the Laplace transform of the solution
Y(s).Y(s). Write the solution as a single
fraction in s.
Y(s)= ______________
B) Find the partial fraction decomposition of Y(s). Enter all
factors as first order terms in s, that is, all terms
should be of the form (c/(s-p)), where c is a constant and the root
p is a constant. Both c and p may be complex.
Y(s)= ____ + ______ +______
C)...
Solve for Y(s), the Laplace transform of the solution y(t) to
the initial value problem below. y'''+7y''+4y'-12y= -24, y(0) = 11,
y'(0)= 5, y''(0) = -43
Use the Laplace transform to solve the following initial value
problem,
y′′ − y′ − 30y = δ(t − 7),y(0) = 0, y′(0) = 0.
The solution is of the form ?[g(t)] h(t).
(a) Enter the function g(t) into the answer box below.
(b) Enter the function h(t) into the answer box below.