Solving Differential Equations with Boundary Conditions

[supermesh]

We have these two equations:
dx/dt = -k1 (y)
dy/dt = k2 x
k1= 10 k2= 10
These are the conditions:
x(0)= 100
y(0) = 0

I am so confused...This is what I have done so far...but is not making any sense...

x= (dy/dt) (1/k2)
Substitute in:

d2y/dt2 = -100 y

So the solution is

Y= c1 cos 10x+ c2 sin 10x

I don't know how to use boundary counditions now...Is this even a right approach?

Thank you so much

 

[Snazzy]

The rule for a differential equation:
\frac{dy}{dt}=ky
y(t)=y_0e^k^t

 

[D H]

x= (dy/dt) (1/k2)
Substitute in:

d2y/dt2 = -100 y

Good so far.

So the solution is

Y= c1 cos 10x+ c2 sin 10x

There is no x in your differential equation; why do you have one here? Try finding the solution to the second order differential equation again.