1. (Consider the differential equationdy/dt=y(1-y^2)(i) Determine the equilibrium solutions.(ii) Obtain the general solution.(iii) Solve the initial-value problem y(0) = 1/2(iv) Draw the phase line.(v) Sketch solution curves in the ty-plane corresponding to the initial conditions y(0) =-3/2; y(0) =1/2;y(0)=3/22. Consider the differential equationDy/dt= -2ty^2.(i) Obtain the general solution.(ii) Find all values of y0 such that the solution to the initial-value problem y(-1) = y0 isdefined for all real t (i. e., find all y0 such that the solution does not blow up in finite time.)

attached below is the detailed solution

i) equilibrium solution : y = 0 , y^2 = 1 , y = -1 , +1

ii) attached below

iii) attached below

iv) attached below

v) attached below

Step-by-step explanation:

v) For the sketch of curve attached

red curve ( y(0) ) = -3/2

blue curve ( y(0) ) = 1/2

green solution curve ( y(0) ) = 3/2

fahrenheit

step-by-step explanation:

fahrenheit is more precise than celsius. the ambient temperature on most of the inhabited world ranges from -20 degrees fahrenheit to 110 degrees fahrenheit—a 130-degree range. on the celsius scale, that range is from -28.8 degrees to 43.3 degrees—a 72.1-degree range. this means that you can get a more exact measurement of the air temperature using fahrenheit because it uses almost twice the scale.

its an acute right triangle

step-by-step explanation: