I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
I have an equation that looks like
##i\dot{\psi_n}=X~\psi_n+\frac{C~\psi_n+D~a~\psi^\ast_{n+1}+E~b~\psi_{n+1}}{1+\beta~(D~\psi^\ast_{n+1}+E~\psi_{n+1})}##
where ##E,b,D,a,C,X## are constants. I have the ansatz
##\psi_n=A_n~e^{ixt}+B^\ast_n~e^{-itx^\ast}##, ##x## and ##A_n,B_n## are complex...
Homework Statement
y(w)= 3/(iw-1)^2(-4+iw)
Homework Equations
N/A
The Attempt at a Solution
3/(iw-1)^2(-4+iw)
= A/iw-1 + B/(iw-1)^2 + C/-4+iw
for B iw = 1
B=3/-4+1 = -1
for C iw = 4
C= 3/(4-1)^2 = 1/3
I know the answer for A should be -1/3 however I am unsure how to obtain this as if the...
Hello, I am enrolled in calculus 2. Just having started a section in our text book about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem:
∫ 1/(x^2+1)dx
I immediately...
Homework Statement
The question is stated at the top of the attached picture with a solution
20160303_095831.jpg
The correct results of the coefficients are A=2, B=-5, C=1
I have tried this problem multiple times and am still getting ugly coefficients. I have no idea why. A fresh pair of eyes...
Homework Statement
Decompose \frac{2(1-2x^2)}{x(1-x^2)}
I get A = 2, B =-1, C = 1, but this doesn't recompose into the correct equation, and the calculators for partial fraction decomposition online all agree that it should be A = 2, B = 1, C = 1.
Here is one of the online calculator results...
Homework Statement
I want to express the following expression in its Taylor expansion about x = 0:
$$
F(x) = \frac{x^{15}}{(1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)}
$$
The Attempt at a Solution
First I tried to rewrite the function in partial fractions (its been quite a while since I've last...
Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)?
When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...