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

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1use the formula D(e^u)= e^u D(u) lets see what will you get

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

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

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

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1sorry about that i dint solved it my self but im just guiding you to the right solution :D

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

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

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

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

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1hmm 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

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0If you have 3e^2t and the 2 comes down, wont you have +2 multiplying by 3 = 6? :D

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

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0Any ideas how to start it? Aren't we back where we started?

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

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

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

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0I know i have to derive that. But not sure how to start

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

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

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

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1yeah 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
 2 years ago
Best ResponseYou've already chosen the best response.0? Don't know what you mean

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1just plug in the one you just solve to the formula d^2y/dt^2 +6 dy/dt +8y =0 _________ +6(_______) +8(________) =0

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

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

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry this is taking so long, I got A in my last 3 engineering differentiation exams, but just not getting this one

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0But how can you say it's equal to zero if you have T and Y still in the equation?

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.16 dy/dt =6( 20 e^4t 3e^2t )= 120 e^4t 18 e^2t

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

Asylum15
 2 years ago
Best ResponseYou've already chosen the best response.0But T has no value, no given value, so I can't say for example 80^4t = 0!?

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

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1yup it has no value its like this 10 e^ 7t  10 e^ 7t = 0 e^ 7t=0

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1just 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
 2 years ago
Best ResponseYou've already chosen the best response.040e^4t + 24e^2t + 8y = 0

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1d^2y/dt^2 +6 dy/dt + 8y =? (80e^4t  12e^2t) +6(20e^4t +6e^2t) + 8( 5e^4t 3e^2t)=?

mark_o.
 2 years ago
Best ResponseYou've already chosen the best response.1d^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
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