
#1
Aug2305, 06:28 AM

P: 60

How to reduce the equation: Show how the equation u(t)+Int( 0>t) {[e^a(tt1)]u(t1)}dt1 = k can be reduced to a differential equation and obtain an intial condidtion for the equation.
Remarks: Int(0>t): integral from 0 to t ! 



#2
Aug2305, 08:02 AM

Sci Advisor
HW Helper
PF Gold
P: 12,016

Evaluate your equation at t=0. What does that say about u(0)?
Differentiate your equation to get your differential equation. 



#3
Aug2305, 09:36 AM

P: 60





#4
Aug2305, 10:00 AM

HW Helper
P: 2,168

how to reduce?[tex]\frac{d}{dt}\int_{a(t)}^{b(t)}f(x,t)dx=\int_{a(t)}^{b(t)} \partial_tf(x,t)dx+f(x,t)\partial_tx_{x=a(t)}^{x=b(t)}[/tex] [tex]\frac{d}{dt}\int_{a(t)}^{b(t)}f(x,t)dx=\int_{a(t)}^{b(t)} \frac{\partial}{\partial t}f(x,t)dx+f(x,t){\partial x}{\partial t}\right_{x=a(t)}^{x=b(t)}[/tex] http://mathworld.wolfram.com/LeibnizIntegralRule.html for the initial condition you should know that [tex]\int_0^0 f(x) dx=0[/tex] 


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