Taylor Series Approximation for Solving Initial Value Problems

[cscott]

With a simple ODE like $\frac{ds}{dt} = 10 - 9.8t$ and you're given an initial condition of s(0) = 1, when doing the approximation would s'(0) = 10 - 9.8(0), s'' = ... etc?

 

[HallsofIvy]

Yes, you are given s(0) so just plug it into the given equation and solve for s'(0). Actually, the crucial point is under your "etc." Since
s'= 10- 9.8t, s"= -9.8, s"'= 0, etc. It should be no surprise that s is a quadratic function of t.

It would be more interesting if there were an "s" on the right side of the equation.

 

[cscott]

Thanks for the help.