System of equations

[shreddinglicks]

How do I solve the system:

dx/dt = y
dy/dt = -x

I've tried to plug the 2nd equation into the first and integrating but it does not give me the solution in my textbook.

 

[LCKurtz]

Show us what you did and what the book tells you.

 

[shreddinglicks]

The bottom has the solution from the textbook.

 

[LCKurtz]

Your integration is nonsense. For example [MATH]\int \frac 1 y d^2y = \int dt^2[/MATH].
You are okay down to [MATH]y'' = -y [/MATH] or, better, [MATH]y'' + y = 0[/MATH]. That is a constant coefficient DE. Have you studied how to solve those? Starting with [MATH]y = e^{rt}[/MATH], and getting the characteristic equation. You should wind up with the expected sine and cosines.

 

[shreddinglicks]

It's been a long time, thanks.