Asylum15
Differentiation Question! :(
Delete
Share
This Question is Closed
Asylum15
Best Response
You've already chosen the best response.
0
If y = \[5e ^{-4t} - 3e ^{-2t}\] show that \[\frac{ d^2y }{ dt^2 } + 6\frac{ dy }{ dt } +8y = 0\]
Asylum15
Best Response
You've already chosen the best response.
0
Derive Y?
mark_o.
Best Response
You've already chosen the best response.
1
use the formula
D(e^u)= e^u D(u) lets see what will you get
Asylum15
Best Response
You've already chosen the best response.
0
So Y' = -4(5e^-4t) + 2 (-3e^-2t) ?
Asylum15
Best Response
You've already chosen the best response.
0
e^ax = ae^ax
mark_o.
Best Response
You've already chosen the best response.
1
De^ax = ae^ax yup
Asylum15
Best Response
You've already chosen the best response.
0
So my first step is correct?
mark_o.
Best Response
You've already chosen the best response.
1
ah +3
Asylum15
Best Response
You've already chosen the best response.
0
\[= -4(5e ^{-4t}) + 2(-3e ^{-2t})\]
Asylum15
Best Response
You've already chosen the best response.
0
?
mark_o.
Best Response
You've already chosen the best response.
1
sorry about that i dint solved it my self but im just guiding you to the right solution :D
Asylum15
Best Response
You've already chosen the best response.
0
So am i right so far?
mark_o.
Best Response
You've already chosen the best response.
1
yes correct :D
Asylum15
Best Response
You've already chosen the best response.
0
Ok, what should I do next? :)
mark_o.
Best Response
You've already chosen the best response.
1
now do the 2nd derivative
Asylum15
Best Response
You've already chosen the best response.
0
Y'' yeah?
mark_o.
Best Response
You've already chosen the best response.
1
yup but you can still simplify that one by multiplying the constant coefficients
Asylum15
Best Response
You've already chosen the best response.
0
-4 multipled by 5e ?
Asylum15
Best Response
You've already chosen the best response.
0
Why is the 5e on the first line a -?
mark_o.
Best Response
You've already chosen the best response.
1
hmm do it like this
5e^-4t -3e^-2t
=5e^-4t D(-4t) -3e^-2tD-2t)
=5(-4)e^-4t -3(-2)e^-2t
=-20e^-4t +6e^-2t
Asylum15
Best Response
You've already chosen the best response.
0
If you have -3e^-2t and the -2 comes down, wont you have +2 multiplying by -3 = -6? :D
mark_o.
Best Response
You've already chosen the best response.
1
its -3(-2)=+6
Asylum15
Best Response
You've already chosen the best response.
0
Oh :D
mark_o.
Best Response
You've already chosen the best response.
1
but for +3(-2)=-6
Asylum15
Best Response
You've already chosen the best response.
0
Sorry, so now do the 2nd derivative of this?
mark_o.
Best Response
You've already chosen the best response.
1
yeah try that
Asylum15
Best Response
You've already chosen the best response.
0
Any ideas how to start it? Aren't we back where we started?
Asylum15
Best Response
You've already chosen the best response.
0
I need to get an a/b no?
mark_o.
Best Response
You've already chosen the best response.
1
if
y'=-20e^-4t +6e^-2t
what is y" ?
mark_o.
Best Response
You've already chosen the best response.
1
or for example if
y=-20e^-4t +6e^-2t
what is dy/dx?
Asylum15
Best Response
You've already chosen the best response.
0
I know i have to derive that.
But not sure how to start
Asylum15
Best Response
You've already chosen the best response.
0
Do you use the same rule again?
mark_o.
Best Response
You've already chosen the best response.
1
do the same thing as you did on the first one
Asylum15
Best Response
You've already chosen the best response.
0
ah
mark_o.
Best Response
You've already chosen the best response.
1
yup the same rule applies to it
Asylum15
Best Response
You've already chosen the best response.
0
80e^-4t - 12e^-2t
mark_o.
Best Response
You've already chosen the best response.
1
yeah correct :D
now do some multiplication and addition or subtraction using the formula
to prove
the one you wrote down above
the d^2y/dx^2
Asylum15
Best Response
You've already chosen the best response.
0
? Don't know what you mean
mark_o.
Best Response
You've already chosen the best response.
1
just plug in the one you just solve to the formula
d^2y/dt^2 +6 dy/dt +8y =0
_________ +6(_______) +8(________) =0
mark_o.
Best Response
You've already chosen the best response.
1
_________ +6(_______) +8(________) =? solve it and see if you will get zero
Asylum15
Best Response
You've already chosen the best response.
0
But Don't i have a t?
mark_o.
Best Response
You've already chosen the best response.
1
its like 6 dy/dt
6( -20 e^-4t -3e^-2t ) multiply it
Asylum15
Best Response
You've already chosen the best response.
0
Sorry this is taking so long, I got A in my last 3 engineering differentiation exams, but just not getting this one
Asylum15
Best Response
You've already chosen the best response.
0
But how can you say it's equal to zero if you have T and Y still in the equation?
mark_o.
Best Response
You've already chosen the best response.
1
6 dy/dt =6( -20 e^-4t -3e^-2t )= -120 e^-4t -18 e^-2t
mark_o.
Best Response
You've already chosen the best response.
1
you will add or subtract like terms like 100 e^ 7t + 50 e^ 7t = 150 e^ 7t
Asylum15
Best Response
You've already chosen the best response.
0
But T has no value, no given value, so I can't say for example 80^-4t = 0!?
Asylum15
Best Response
You've already chosen the best response.
0
I don't know T! :P
Asylum15
Best Response
You've already chosen the best response.
0
Using your method I have : -40e^-4t + 24e^-2t + 8y = 0
mark_o.
Best Response
You've already chosen the best response.
1
yup it has no value its like this 10 e^ 7t - 10 e^ 7t = 0 e^ 7t=0
mark_o.
Best Response
You've already chosen the best response.
1
just plug in the one you just solve to the formula
d^2y/dt^2 +6 dy/dt + 8y =?
I I I
V V V <------- arrow down pointing it solve them
(_____________)+ 6(_________) + 8(_______)= __________ 0 ?
Asylum15
Best Response
You've already chosen the best response.
0
-40e^-4t + 24e^-2t + 8y = 0
Asylum15
Best Response
You've already chosen the best response.
0
:D
mark_o.
Best Response
You've already chosen the best response.
1
d^2y/dt^2 +6 dy/dt + 8y =?
(80e^-4t - 12e^-2t) +6(-20e^-4t +6e^-2t) + 8( 5e^-4t -3e^-2t)=?
mark_o.
Best Response
You've already chosen the best response.
1
d^2y/dt^2 + 6 dy/dt + 8y =?
(80e^-4t - 12e^-2t) + 6(-20e^-4t +6e^-2t) + 8( 5e^-4t -3e^-2t)=? solve by
multiplying first the 6 times the value of dy/dt also 8 times the value of y then add or
subtract like terms