Question

why the functions with this graph cannot be solution to this differential equation?

Answer 1

y'(t) = 0, when y = 1
so, y(t) must have a stationary point when y = 1. however in second graph, the graph is rising when it reaches 1. so second graph cannot be the solution

Answer 2

also, observe that y'(t) is always >= 0
cuz product of exponent and square never produce a negative.

so that tells us, y(t) is an 'increasing funciton'
however the first graph is decreasing after t=2. so first graph cannot be a solution either

Answer 3

@ganeshie8, thank you! that clears my mind(: