The MSP430 RTOS I wrote was real-time and cooperative, with the caveat that it was application specific, and no task would ever take more than one millisecond to complete. I was careful to design all the tasks so they would never exceed the maximum run-time. For the tasks that needed more time, I broke them into several sub-tasks.
You said; "When you set a timer, which stops the running task to switch "to somewhere else", then it's not cooperative." You are correct. The OS does not require the cooperation of the task in order to suspend it and start/resume a different task. A non-cooperative OS does not require the task to either make a system call (such as waiting on I/O) or to finish. It will preempt the running task according to the scheduler rules. Typically a scheduler will receive periodic interrupts so that it can assess which task should be made active. On real-time systems without much processing headroom, the context switching between tasks can take up a significant percentage of CPU time, which is why I went with cooperative multitasking on the (25MHz) MSP430 micro-controller.
You said; "When you set a timer, which stops the running task to switch "to somewhere else", then it's not cooperative." You are correct. The OS does not require the cooperation of the task in order to suspend it and start/resume a different task. A non-cooperative OS does not require the task to either make a system call (such as waiting on I/O) or to finish. It will preempt the running task according to the scheduler rules. Typically a scheduler will receive periodic interrupts so that it can assess which task should be made active. On real-time systems without much processing headroom, the context switching between tasks can take up a significant percentage of CPU time, which is why I went with cooperative multitasking on the (25MHz) MSP430 micro-controller.