Question

Given `(dr)/(dt)=(sect,tant,t^2)` calculate `r(t)` such that `r(0) = (0,0,3)` ?

Answer 1

See below.

Explanation:

If `(dr)/(dt)=(sect,tant,t^2)` then

`r = int (sect,tant,t^2)dt = (log(cos(t/2)+sin(t/2))-log(cos(t/2)-sin(t/2)),-log(cos(t)),1/3t^3)+(C_1,C_2,C_3)`

The initial conditions are

`r(0)=(0,0,0)+(C_1,C_2,C_3)=(0,0,3)` so the solution is

`r(t)= (log((cos(t/2)+sin(t/2))/(cos(t/2)-sin(t/2))),-log(cos(t)),1/3t^3+3)`