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Diff Eq 7.1

 

<== Differential Equations
Number Question Answer
See the work
1. Find the Laplace transform of the following functions:

1. f(t)= -9 \sqrt{t} + 1 t
F(s)= .

2. f(t) = 12 t^{3/2} - e^{-6 t}
F(s)= .

3. f(t) = \sin(10 t) + \cos (10 t)
F(s)= .

1. F(s)=

2.F(s)=

3.F(s)=
The work
2. Find the Laplace transform of the following functions:

1. f(t)= \sin(5 t) \cos(5 t)
F(s)= .

2. f(t) =\cos^2 (5 t)
F(s)= .

3. f(t) = (5  - 2 t)^2
F(s)= .

1. F(s)=

2.F(s)=

3.F(s)=
The work
3. Find the inverse Laplace transform of
rac{7 s +3}{s^2 + 11} \hspace{0.5in} s > 0

y(t)= .
y(t)= The work
4. Find the inverse Laplace transform of
rac{3 s +6}{s^2 - 16} \hspace{0.5in} s > 4

y(t)= .
y(t)= The work
5. Find the Laplace transform of
f(t) = -2 u_{5}(t)  - 3 u_{6}(t)  - 6 u_{9}(t)

F(s)= .
F(s)= The work
6. Find the inverse Laplace transform of
F(s) = rac{-1 e^{-3 s} - 2 e^{-4 s} - 2 e^{-7 s} - 5 e^{-10 s}}{s}

f(t) = . (Use step(t-c) for u_c(t) .)
f(t) = The work
7. Find the Laplace transform of
f(t) = 6 u_{2}(t)  - 1 u_{3}(t) + 3 u_{5}(t)

F(s)= .
F(s)= The work
8. Consider the function
f(t) = \begin{cases}              6, & 0 \leq t < 1 \cr               -6, & 1 \leq t < 4 \cr               4, & t \geq 4              nd{cases};

1. Write the function in terms of unit step function
f(t) = . (Use step(t-c) for u_c(t) .)

2. Find the Laplace transform of f(t)
F(s)= .

f(t) =
F(s)=
The work