MaplePrimes - answers and comments on Question, How to make a convolution with diff

You don't tell us what f is, but my guess

Preben Alsholm — Thu, 24 Nov 2011 20:05:47 Z

You don't tell us what f is, but my guess is

f:=x->-1+exp(-x);

#So you can do as follows
int(diff(f(x),x)*f(t-x),x=0..t);
combine(expand(%));

Or using the laplace transform and assuming that f(0) = 0 we can find f:

f:='f':
A:=int(diff(f(x),x)*f(t-x),x=0..t);
with(inttrans);
eq:=laplace(A,t,s) = laplace(1-exp(-t)-t*exp(-t),t,s);
solve(eq,{laplace(f(t),t,s)});
map(invlaplace,subs(f(0)=0,[%]),s,t);

Sorry, f is

nic_rf — Thu, 24 Nov 2011 20:38:33 Z

f(0) = 0

f'(0) > 0

1-exp(-t)

Preben Alsholm — Thu, 24 Nov 2011 21:27:53 Z

@nic_rf Well, then f(t) = 1-exp(-t) is the solution. The laplace transform method using f(0) = 0 gave two possible solutions, but with f ' (0) > 0 one is singled out, i.e. f(t) = 1-exp(-t).