Question

Differential Equations

Please check question below (with solution)

Answer 1

\(\mathcal L \lbrace \psi (t) \rbrace\) where \(\psi (t) = 4 \quad \quad 0< t < 1\)
\(= 3 \quad \quad \; \;\;\;\;\;t>1\)

My solution:
\[\int_0^1 4(e^{-st})dt + \int_1^{\infty} 3(e^{-st}) dt\]
\[\large \left[-\frac{4e^{-st}}{s} \right|_0^1 + 3 \left[-\frac{e^{-st}}{s}\right |_1^{\infty}\]
\[\large -\frac{4e^{-s}}{s} + \frac 4s - \frac{3e^{-s}}{s} \implies - \frac{7e^{-s}}{s} + \frac 4s \implies \frac{-7e^{-s} + 4}{s}\]

Answer 2

Limits should be:

\(0 \le t \le 1\)

for first part I guess..

Answer 3

heh?

Answer 4

so you're saying im wrong?

Answer 5

Don't you think last term should be positive??

Answer 6

which last term?

Answer 7

..that...is...a...good...point...

Answer 8

Where you plugged 1 as a lower limit ..

Answer 9

so it should be \[\large \frac{-e^{-s}+4}{s}\]

Answer 10

Yep..

Answer 11

everything else is right?

Answer 12

For me it is okay..

Answer 13

THANKS!

Answer 14

Welcome and Well Done..