Below we see the slope field of an ODE y′=F(y)y' = F(y)y′=F(y) with three stationary solutions.
y′=F(y)y' = F(y)y′=F(y)
Which convergence behavior does the solution y\color{orange}yy with y(−5)=5\color{orange}y(-5) = 5y(−5)=5 exhibit?
y\color{orange}yy
y(−5)=5\color{orange}y(-5) = 5y(−5)=5
limt→+∞=4\lim\limits_{t \to + \infty} = 4t→+∞lim=4
limt→+∞=+∞\lim\limits_{t \to + \infty} = + \inftyt→+∞lim=+∞
limt→+∞=−∞\lim\limits_{t \to + \infty} = - \inftyt→+∞lim=−∞
limt→+∞=1\lim\limits_{t \to + \infty} = 1t→+∞lim=1