Solve Difference Equation | General Solution | No Particular Solution

haoku
Messages
24
Reaction score
0

Homework Statement


Given difference equation
T(a+2)-7T(a+1) +6T(a)= 6f
Find the general solution of this equation

Homework Equations


I have found the auxiliary equation be
A(1)^n+B(6)^n
But seems can't find the particular solution of that question.
Is it impossible to do this question?


The Attempt at a Solution

 
Physics news on Phys.org
Hi haoku! :smile:
haoku said:
T(a+2)-7T(a+1) +6T(a)= 6f

What's f? :confused:
 
f is a constant? Then "trying" a constant as solution won't work because a constant already satisfies the homogeneous equation (n0= 1). Try T(n)= Cn as a solution and determine C.
 
Sorry this is 6a
 
haoku said:
Sorry this is 6a

ah! :biggrin:

in that case, try a polynomial in a. :smile:​
 

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

Solving differential equation (t^2-1)y''-6y=1
Replies
2
Views
826
Solve (t^2-1)y'' +4ty'+2y=6t, given two particular solutions
Replies
2
Views
919
Frequencies for harmonic oscillator with multiple periodic solutions?
Replies
6
Views
1K
How to get general solution via Green's function?
Replies
1
Views
2K
Diff. Eq. — Identifying Particular Solution Given solution family
Replies
4
Views
2K
How to find a system of equations when the solution is given?
Replies
6
Views
2K
Prove that solutions to autonomous first order DE can't have local maxima
Replies
2
Views
1K
Finding the Particular solution to a Diff. Eq. System
Replies
8
Views
2K
General solution vs particular solution
2
Replies
52
Views
7K
Avoid unpleasant integrals in solving IVP
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top