1
vote
2answers
83 views

Solve second order differential equation with Heaviside function using Laplace transform

The equation is: $$y'' + 3y = u_4(t)\cos(5(t-4)), \quad y(0) = 0, \quad y'(0) = -2$$ Here $u_4$ is the Heaviside function with activation switch at $t=4$. I can get all the way to the partial ...
0
votes
2answers
83 views

Laplace question continued (partial fractions)

Last night I attempted and successfully finished (with the help of stackexchange) the first part to this question on laplace transformations: Laplace question - help needed The second part to this ...
3
votes
1answer
51 views

How do I apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$?

I want to apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$. I'm not able to do it in the standard way, because one term has $z^{-1}$ term and the other has $z$. What is the approach ...
2
votes
1answer
85 views

Basic Partial Fractions

I feel super foolish asking this, but I've reached a mental block. I'm trying to find the inverse laplace transform of: $$\frac{s+3}{(s + 1)^2 (s-2)}$$ but, when I expand it into partial ...
2
votes
1answer
50 views

Help with partial fraction decomposition

So I was working on problem 16 in Elementary Differential Equations 9th edition by DiPrima and I get to the point where I'm using partial fraction's to separate : $\displaystyle {1 \over ...
1
vote
1answer
85 views

Laplace inverse of $\frac{e^{-s}(3s^2-s+2)}{(s-1)(s^2+1)}$

I thought maybe you could fist solve $\frac{(3s^2-s+2)}{(s-1)(s^2+1)}$ using partial fractions and later solve the $e^{-s}$ separately as it is a $d(t-1)$ (Dirac delta function). As you solve the ...
3
votes
1answer
105 views

Help with a partial fraction decomposition

One of my homework problems last week was to find the inverse Laplace transform of the following: $$F(s)=\frac{2s+1}{s^2-2s+2}.$$ The answer is $f(t)= 2e^t \cos t + 3e^t \sin t$. Obviously once ...
0
votes
2answers
106 views

Partial fraction with same denominator

Is the following fraction (actually a Laplace transform) a kind of partial fraction? $$\frac{4s+3}{{s^2}+3}$$ Can this be solved this way? $$\frac{A}{s}+\frac{B}{s+{\frac{3}{s}}}$$ If not can you ...
1
vote
3answers
919 views

Inverse Laplace transform with partial fraction

I have the transform below: $$\frac{(7s+2)(2s-5)}{{s^2}(s-2)}$$ I think this is should be partial fraction to be solved. Can you please help me figure how to consider A, B, C and denominators?
1
vote
1answer
213 views

Using z-transforms to solve difference equations.

I am faced with the following question and would appreciate any help you may be able to offer: It is not homework, I know the first and second shift theorems and based on the other examples I have ...