What is the Solution for Undetermined Coefficients of y''+y'+y=(1-e^-t)?

  • Thread starter Thread starter kraigandrews
  • Start date Start date
kraigandrews
Messages
105
Reaction score
0

Homework Statement



I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t)

my guess is A-Ae^-t but I am not sure
 
Physics news on Phys.org
kraigandrews said:

Homework Statement



I am stuck on this and just need to know the form of the solution for undetermined coeffecients of y''+y'+y=(1-e^-t)

my guess is A-Ae^-t but I am not sure
Well, what happened when you tried to work with your guess?
 
it didnt work but i was just wondering if the 1 matters.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Variation of parameter VS Undetermined Coefficients
Replies
7
Views
2K
How to get general solution via Green's function?
Replies
1
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
2K
Solving differential equation (t^2-1)y''-6y=1
Replies
2
Views
821
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
Replies
2
Views
2K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
Replies
7
Views
2K
Solving Systems of Inhomogeneous Linear ODEs
Replies
3
Views
2K
Is f(t,y)=e^{-t}y Lipschitz Continuous in y?
Replies
1
Views
2K
Prove that solutions to autonomous first order DE can't have local maxima
Replies
2
Views
1K
Method of undetermined coefficients -- Help please
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top