Differential equation using laplace

seang
Messages
184
Reaction score
0

Homework Statement


How do I solve the following differential equation with the Laplace Transform:?
f(t)'' - a*f(t) = 0 (all ICs are equal to zero).



Homework Equations





The Attempt at a Solution



So, I get something like F(s)*(s^2 - a) = 0. I don't know where to go from there.
 
Physics news on Phys.org
Your equation is missing terms which correspond to the boundary behavior of f(t). F(s)=0 is not the only solution.
 
Hmmm. If as you say all IC's are 0. f(0)=f'(0)=0. Then f(t)=0 is the only solution. Pretty trivial use of laplace transforms.
 

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

Laplace transform of cosine squared function
Replies
1
Views
1K
What is the Inverse Laplace Transform of e^(-sx^2/2)?
Replies
10
Views
2K
Find the particular solution of the second order differential equation
Replies
3
Views
2K
Given unit impulse response, obtain differential equation
Replies
7
Views
1K
Does the Laplace Transform of e^(at)/t Exist?
Replies
4
Views
2K
Laplace transform applied to a differential equation
Replies
1
Views
1K
Finding the Laplace transform of a piecewise function
Replies
3
Views
1K
Characteristic equation in terms of the Laplace operator
Replies
26
Views
5K
Show uniqueness in Dirichlet problem in unit disk
Replies
6
Views
1K
Mellin transform of Dirac delta function ##\delta(t-a)##
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top