Inital Values problems

[FizzyCrow]

Hi, i have to solve these inital value problems, however there is no explanation on how to do so in my book, or from my prof, so any help would be appreciated



r, i, j, and k are vectors

dr/dt=1/t^2+1i - 1/the square root of 1-t^2j + t/the square root of t^2 +1k r=j+k

d^2r/dt^2= -2i -4j, dr/dt= di and r=3j when t=1


sorry about the notation, i don't know how to get it on a computer, help with that too would be appreciated

Thanks a bunch!

 

[soroban]

Hello, FizzyCrow!

You simply MUST learn to use parentheses!
Your stuff is impossible to read . . . but I'll make some wild guesses . . .

r, i, j, and k are vectors

. dr . . . . . .1 . . . . . . . 1 . . . . . . .t
. --- . = . ------- i - -<u>------</u>- j + -<u>--------</u>- k . . r(0) .= .j + k
. dt . . . . t² + 1 . . √1 - t² . . . √t² + 1
.

Integrate: .r(t) .= .(arctan t)i - (arcsin t)j + (t² + 1)^½k + C

Since r(0) = j + k, we have: .r(0) . = . (arctan 0)i - (arcsin 0)j + (0² + 1)^½k + C . = . j + k

. . Then: .k + C .= .j + k . ---> . C = j


Therefore: .r(t) .= .(arcsin t)i - (arcsin t)j + (t² + 1)^½k + j

. . . . . . . . . r(t) .= .(arctan t)i + (1 - arcsin t)j + (t² + 1)^½k
.