Question

Find the particular solution to the differential equation
6(du)/(dt)=u^2
subject to the initial condition u(0)=8

Answer 1

well this is an interesting question, but simple

Answer 2

integrate dx/dt ?

Answer 3

in order to find x(t)

Answer 4

then substitute x(t) in y(t)

Answer 5

hence, differentiate y(t), you get the answer

Answer 6

alright I'll try it

Answer 7

this is a bit different than the normal way students are used to in solving parametric equations

Answer 8

Im a bit confused what I do with dx/dt=3 and x=10

Answer 9

Hint: when you integrate you'll have a constant, so the number is there to help find that constant

Answer 10

ok

Answer 11

\[\int\limits dx = 3 \int\limits dt\]

Answer 12

\[x = 3t + c\]

Answer 13

I am sorry but I dont see how you got that

Answer 14

what level are you at?

Answer 15

Calculus for business

Answer 16

well do you agree if you integrate 3 with respect to t you get 3t + c

Answer 17

yes

Answer 18

well that's all i did x = 3t +c

Answer 19

ok I see, but now how do I use that toward the equation

Answer 20

now you plug in x = 3t +c in y

Answer 21

199 = 3t + c ?

Answer 22

y = 2(3t+c)^2 - 1

Answer 23

now find dy/dt

Answer 24

dy/dt=12t+4c-1?

Answer 25

sorry no "-1"

Answer 26

expand the function first

Answer 27

y=18t^2+4ct+2c^2-1

Answer 28

I thought you had to find the prime first

Answer 29

well you can do so but i am trying to make this as simple as possible

Answer 30

ok

Answer 31

y' = 36t + 12c

Answer 32

2[9t^2+6ct+c^2]-1

Answer 33

now the question is how do you find c?

Answer 34

Yes

Answer 35

well i think you could do that, this is done using simple method of linear equation y = mx +c, in your case y = 3t +c, what do you do to find c?

Answer 36

sorry x = 3t +c

Answer 37

if t = 0 and x =10 what is c?

Answer 38

10

Answer 39

good

Answer 40

your done!

Answer 41

Thank you!

Answer 42

your welcome! it is a good question worth practicing and spending time on it

Answer 43

Yes and I will look over this again after a few more problems, do be sure that I could do it on my own now. Thanks again

Answer 44

I am pretty sure you can, and that makes me happy all the best