Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral before transforming.(Write your answer as a function of s.) {L}{leftlbrace{e}^{{-{t}}}cdot{e}^{t} cos{{left({t}right)}}rightrbrace}

CMIIh 2021-01-05 Answered
Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral before transforming.(Write your answer as a function of s.)
L{etetcos(t)}
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

opsadnojD
Answered 2021-01-06 Author has 95 answers
Step 1
Consider the provided question,
We have to find L{etetcos(t)} Step 2
Now, the given Laplace transform is find as,
L{etetcos(t)}=L{et}+L{etcos(t)}
=(1s+1)s1(s1)2+12[Use,L(eat)=1saandL(eatcosbt)=sa(sa)2+b2]
=s1(s+1)[(s1)2+1]
Thus , L{etetcos(t)}=s1(s+1)[(s1)2+1]
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-04-27
I am trying to take the laplace transform of cos(t)u(tπ). Is it valid for me to treat it as ((cos(t)+π)π)u(tπ) and treat cos(t)π as f(t) and use the 2nd shifting property, or is this not the correct procedure?
asked 2020-12-28
Solve the linear equations by considering y as a function of x, that is
y=y(x)
y2xy=ex2
asked 2021-09-23
Find the inverse Laplace transform of F(s)=7s6s24
asked 2022-01-18
Differential equation f(x)+(n1)(f(x))2sinh(x)=0
asked 2022-05-23
In my differential equations book, I have found the following:
Let P 0 ( d y d x ) n + P 1 ( d y d x ) n 1 + P 2 ( d y d x ) n 2 + . . . . . . + P n 1 ( d y d x ) + P n = 0 be the differential equation of first degree 1 and order n (where P i i 0 , 1 , 2 , . . . n are functions of x and y).
Assuming that it is solvable for p, it can be represented as:
[ p f 1 ( x , y ) ] [ p f 2 ( x , y ) ] [ p f 3 ( x , y ) ] . . . . . . . . [ p f n ( x , y ) ] = 0
equating each factor to Zero, we get n differential equations of first order and first degree.
[ p f 1 ( x , y ) ] = 0 ,   [ p f 2 ( x , y ) ] = 0 ,   [ p f 3 ( x , y ) ] = 0 ,   . . . . . . . . [ p f n ( x , y ) ] = 0
Let the solution to these n factors be:
F 1 ( x , y , c 1 ) = 0 ,   F 2 ( x , y , c 2 ) = 0 ,   F 3 ( x , y , c 3 ) = 0 ,   . . . . . . . . F n ( x , y , c n ) = 0
Where c 1 , c 2 , c 3 . . . . . c n are arbitrary constants of integration. Since all the c’s can have any one of an infinite number of values, the above solutions will remain general if we replace c 1 , c 2 , c 3 . . . . . c n by a single arbitrary constant c. Then the n solutions (4) can be re-written as
F 1 ( x , y , c ) = 0 ,   F 2 ( x , y , c ) = 0 ,   F 3 ( x , y , c ) = 0 ,   . . . . . . . . F n ( x , y , c ) = 0
They can be combined to form the general solution as follows:
F 1 ( x , y , c )   F 2 ( x , y , c )   F 3 ( x , y , c )   . . . . . . . . F n ( x , y , c ) = 0                         ( 1 )
Now, my question is, whether equation (1) is the most general form of solution to the differential equation.I think the following is the most general form of solution to the differential equation :
F 1 ( x , y , c 1 )   F 2 ( x , y , c 2 )   F 3 ( x , y , c 3 )   . . . . . . . . F n ( x , y , c n ) = 0                         ( 2 )
If (1) is the general solution, the constant of integration can be found out by only one IVP say, y ( 0 ) = 0. So, one IVP will give the particular solution. If (2) is the general solution, one IVP might not be able to give the particular solution to the problem.
asked 2021-12-27
A thermometer reading 75F is taken out where the temperature is 20F. The reading is 30F 4 min later.
A. What is the value of k in four decimal places?
B. Find the thermometer reading 7 min after the thermometer was brought outside.
C. Find the time taken for the reading to drop from 75F to within a half degree of the air temperature.
asked 2021-01-15
Show that the first order differential equation (x+1)y3y=(x+1)5 is of the linear type.
Hence solve for y given that y = 1.5 when x = 0

New questions