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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
yeah try that
 2 years 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?
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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