Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Can someone help me with this initial value problem? d^2y over dt^2 = 2/t^3. Given is: dr/dt = t=1 and that whole thing = 1. Another Given is: r(1) = 1. I have no idea how to go about this problem after finding the antiderivative for the d^2r over dx^2.
 2 years ago
 2 years ago
Can someone help me with this initial value problem? d^2y over dt^2 = 2/t^3. Given is: dr/dt = t=1 and that whole thing = 1. Another Given is: r(1) = 1. I have no idea how to go about this problem after finding the antiderivative for the d^2r over dx^2.
 2 years ago
 2 years ago

This Question is Open

frecklesBest ResponseYou've already chosen the best response.1
so you never meant to say anything about y right?
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
So you said you integrated both sides: \[r'=2 \cdot \frac{t^{3+1}}{3+1}+C_1=2 \cdot \frac{t^{2}}{2}+C_1=1 t^{2}+C_1\] => \[r'=\frac{1}{t^2}+C_1\]
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
So we are given r'(1)=1?
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
dr/dt = t=1? r'=t=1 I look at that is when t=1 ,r '=1
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
\[1=\frac{1}{1^2}+C_1 \] Solve for C_1
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
where does the r' come from?
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
Oh! so another way to look at d^2r/dt^2 is r''?
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
Okay! Also just to clarify, when substituting t and r, just plug in one in newly acquired derivative where r and t are respectively? If r(1)=1 and t(1)=2, then plug in respectively and then ... what would happen?
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
well if you are given r'(a)=b then you use the function for r' If t=a then r'=b  and if you are given r(c)=d then use the function r If t=c, then r=d You will use both of this conditions to find your constants
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
So, since r(1)=1, then t(1)=2, then r of t = 1? Somehow I confused myself...
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
I'm sorry to be so blunt
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
No, it makes no sense to me either.
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
You are given r'(1)=1 and r(1)=1
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
r'(1)=1 says when t=1 r'=1
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
\[1=\frac{1}{1^2}+C_1 \] The reason why I wrote this
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
I replaced t with 1 and I replaced r' with 1
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
That makes sense...what happens to the 2 of t(1)=2 tho? how would I solve for C then? Or is it just replace r' with 1 and t with 1?
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
Sorry for all these questions...
 2 years ago

frecklesBest ResponseYou've already chosen the best response.1
I don;t understand where you are seeing t(1)=2?
 2 years ago

sharatheBest ResponseYou've already chosen the best response.0
I added it after getting the orignal problem in the "what happens after" part...cause the next problem was basically this problem, but instead of t(1)=1, it was t(2)=1...Sorry if this was all confusing! I don't quite get how to solve for C when the r' and t equal different numbers but have the same number plugged in...
 2 years ago

ChlorophyllBest ResponseYou've already chosen the best response.2
@sharathe you're confused between the input t = 1, output r' ( 1) = 1 From these input and output => constant C1 = 2
 2 years ago
See more questions >>>
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.