For the autonomous differential equation y\' = f(y), where the graph of f is as
ID: 2893002 • Letter: F
Question
For the autonomous differential equation y' = f(y), where the graph of f is as shown. i) What are the equilibrium solutions? a.) y = plusminus 1, plusminus 2 b.) y = plusminus 1, plusminus 0 c.) y = plusminus 0, plusminus 2 d.) y = 0, plusminus 1, plusminus 2 ii.) Find the limiting behavior of the solution for the initial condition y(0) = 3/2 ii.) a.) lim x rightarrow infinity y(x) = 2: lim x rightarrow infinity y(x) = 1 b.) lim x rightarrow infinity y(x) = 2: lim x rightarrow infinity y(x) = 1 c.) lim x rightarrow infinity y(x) = -2: lim x rightarrow infinity y(x) = 2 d.) lim x rightarrow infinity y(x) = -2: lim x rightarrow infinity y(x) = 2 Do any two. i) Evaluate: integral Squareroot 1 - x/x dx a.) Squareroot x - x^2 + sin^-1(Squareroot x) + c b.) Squareroot x + x^2 + sin^-1(Squareroot x) + c c.) Squareroot x - x^2 - sin^-1(Squareroot x) + c d.) Squareroot x + x^2 - sin^-1(Squareroot x) + c Find the centroid of the region bounded by y = e^x, y = 0, x = 0, x = 1. a.) (x, y) = (1/(e - 1), (e + 1)/4) b. (x, y) = (1/(e + 1), (e + 1)/4) c.) (x, y) = (1/(e - 1), (e - 1)/4) d.) (x, y) = (1/(1 - e), (e + 1)/4)Explanation / Answer
Equilibrium solutions means where the fuction attains a value of 0;
From the graph, f(y) =0 at y= 1 , 2 , -1 , -2
Thus, from the options, the correct choice is : option a