- $dy/dt = my+2m-y$
- $dy/dt = (1+y/y)m^2+\cos(\alpha m)$ {where $\alpha$ is a constant}
I have tried to solve 1 but I did not get too far. I began with the 'my' term as it is the only term that is non-linear.
therefore $$\frac{dy}{dt} = my_{ss} + \frac{\partial(my)}{\partial y}\cdot (y-y_{ss}) + \frac{\partial(my)}{\partial m}\cdot (m-m_{ss}) $$
$$m_{ss} y_{ss}+m_{ss}\cdot y'+y_{ss}\cdot m'$$
$dy/dt = m_ss*y_ss+m_ss*y'+y_ss*m'+2m-y$
$dy/dt (at s.s) = m_ss*y_ss+m_ss*y$ as $y = y - y_ss = 0.$
$dy/dt - dy/dt (at s.s) = dy'/dt = m_ss*y_ss+m_ss*y'+y_ss*m'+2m-y-m_ss*y_ss... = m_ss*y'+y_ss*m'+2*m'-y' $
{where s.s means steady state} but I'm not sure if I'm on the right track or where to go from there.
As for q2, as there are 2 variables present, I am unsure where to even begin. An explanation, walk through or any help would be greatly appreciated.