A community for students.
Here's the question you clicked on:
 0 viewing
Asylum15
 2 years ago
Differentiation Question! :(
Asylum15
 2 years ago
Differentiation Question! :(

This Question is Closed

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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.