Can someone check my answer for solving for the initial value expression of the following:
((d^2)s)/(ds^2) -4sin(2t - pi/2), with dt/ds=100 & s=0, @ t=0.

I got: "s = 4sin(2t + pi/2) + 100t + 4". Is this correct?

Any and all help is greatly appreciated :)

Question

Can someone check my answer for solving for the initial value expression of the following: 
((d^2)s)/(ds^2) -4sin(2t - pi/2), with dt/ds=100 & s=0, @ t=0.
 
I got: "s = 4sin(2t + pi/2) + 100t + 4". Is this correct?

Any and all help is greatly appreciated :)

anonymous · Answer

Could you please clarify? I'm not sure what your equation is. I think you mean
$$\frac{d^2s}{dt^2}-4\sin\left(2t+\frac{\pi}{2}\right)\frac{ds}{dt}=100$$
but not certain.

amonoconnor · Answer

I think you are very close to what  I meant. The dt/ds was just a condition, or something to use later, and not meant to be in any way another term of the original second derivative.

mathmale · Answer

Amon, my suggestion would be that you differentiate your own result (s = 4sin(2t + pi/2) + 100t + 4) twice.  If the 2nd derivative of your result is the same as the d. e. from which you began, you're right.  I'll go thru the integration with you again, if you like, but please differentiate your result first.

anonymous · Answer

I'm confused as to why you have $\dfrac{dt}{ds}$ when the solution apparently depends on $t$, and not $s$. Care to explain?