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Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
If y = \[5e ^{4t}  3e ^{2t}\] show that \[\frac{ d^2y }{ dt^2 } + 6\frac{ dy }{ dt } +8y = 0\]
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Derive Y?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
use the formula D(e^u)= e^u D(u) lets see what will you get
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
So Y' = 4(5e^4t) + 2 (3e^2t) ?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
e^ax = ae^ax
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
De^ax = ae^ax yup
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
So my first step is correct?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
\[= 4(5e ^{4t}) + 2(3e ^{2t})\]
 one year ago

mark_o. Group TitleBest ResponseYou'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
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
So am i right so far?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
yes correct :D
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Ok, what should I do next? :)
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
now do the 2nd derivative
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Y'' yeah?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
yup but you can still simplify that one by multiplying the constant coefficients
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
4 multipled by 5e ?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Why is the 5e on the first line a ?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
hmm do it like this 5e^4t 3e^2t =5e^4t D(4t) 3e^2tD2t) =5(4)e^4t 3(2)e^2t =20e^4t +6e^2t
 one year ago

Asylum15 Group TitleBest ResponseYou'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
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
its 3(2)=+6
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
but for +3(2)=6
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Sorry, so now do the 2nd derivative of this?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
yeah try that
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Any ideas how to start it? Aren't we back where we started?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
I need to get an a/b no?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
if y'=20e^4t +6e^2t what is y" ?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
or for example if y=20e^4t +6e^2t what is dy/dx?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
I know i have to derive that. But not sure how to start
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Do you use the same rule again?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
do the same thing as you did on the first one
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
yup the same rule applies to it
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
80e^4t  12e^2t
 one year ago

mark_o. Group TitleBest ResponseYou'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
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
? Don't know what you mean
 one year ago

mark_o. Group TitleBest ResponseYou'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
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
_________ +6(_______) +8(________) =? solve it and see if you will get zero
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
But Don't i have a t?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
its like 6 dy/dt 6( 20 e^4t 3e^2t ) multiply it
 one year ago

Asylum15 Group TitleBest ResponseYou'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
 one year ago

Asylum15 Group TitleBest ResponseYou'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?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
6 dy/dt =6( 20 e^4t 3e^2t )= 120 e^4t 18 e^2t
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
you will add or subtract like terms like 100 e^ 7t + 50 e^ 7t = 150 e^ 7t
 one year ago

Asylum15 Group TitleBest ResponseYou'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!?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
I don't know T! :P
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
Using your method I have : 40e^4t + 24e^2t + 8y = 0
 one year ago

mark_o. Group TitleBest ResponseYou'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
 one year ago

mark_o. Group TitleBest ResponseYou'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 ?
 one year ago

Asylum15 Group TitleBest ResponseYou've already chosen the best response.0
40e^4t + 24e^2t + 8y = 0
 one year ago

mark_o. Group TitleBest ResponseYou'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)=?
 one year ago

mark_o. Group TitleBest ResponseYou'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
 one year ago
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