Question

solve differential equation with an initial condition..

Answer 1

\[dr/dt=(tsint)i+2j+t/\sqrt{1+t ^{2}} k\]

Answer 2

r(0)=i+j-k

Answer 3

don't we just integrate?

Answer 4

r(t)=(-tcost+sint)i+(2t)j+\[\sqrt{1+t ^{2}}\]

Answer 5

yes, and then....what do i do with the initial position?

Answer 6

forgot "k" after sqrt up there

Answer 7

this is just first one
(-tcost+sint)+C

if t equals to zero

(-tcost+sint)+C
0 +C= 1 i

which mean C=1

Answer 8

It's a parametric function of t, with three direction vectors i,j,&k.
Integrate separately (each direction) and use the integration constant to satisfy the initial conditions.

Answer 9

i think r(0)=(1-tcost+sint)i+(1+2t)j-(1+sqrt(1+t^2))k
not sure about k component, is it right?

Answer 10

sqrt(1+0^2)=1

Answer 11

thx