Question

Does anyone know how to solve inital value problems calc 1 or 2

Answer 1

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e61a0f10b8b1f45b4a6ca42

Answer 2

This is a second order, autonomous ODE. We have
\[ \frac{d^2s}{dt^2}=-16 \cos( 4t + \pi ), \]where
\[s'(0)=400,\]\[s(0)=0.\]Autonomous ODEs can be solved by simple integration, as follows:
\[ \int \int \frac{d^2s}{dt^2} = \int \int -16 \cos( 4t + \pi ), \]\[ \int \frac{ds}{dt} = \int -4 \sin( 4t + \pi ) + c_{1}, \]\[ s = \cos( 4t + \pi ) + c_{1}t + c_{2}. \]All you have to do now is solve for both c1 and c2, as follows:
\[\frac{ds}{dt}=-4\sin(4t+\pi)+c_{1},\]\[400=-4\sin(4(0)+\pi)+c_{1},\]\[400=-4\sin(\pi)+c_{1},\]\[c_{1}=400.\]\[s=\cos(4t+\pi)+tc_{1}+c_{2},\]\[0=\cos(4(0)+\pi)+(0)c_{1}+c_{2},\]\[0=\cos(\pi)+c_{2},\]\[0=-1+c_{2},\]\[c_{2}=1.\]Therefore, we find our solution to be:
\[s=\cos(4t+\pi)+400t+1.\]

Answer 3

thank you so much across, your the best