Question

1. Find the equation for each directional field in the list of given equations bellow: di =y+y = y2-y (m) sdy = y® + y2 (iv) a = 2 – 12 (w) ay = 14 +592 (van) ay = 12 +?y (vi) =+ty (vin) = -2 -2 NO -4 -2 0 2

Answer 1

sol:

Using Octave program direction fields are plotted for each differential equation given

(i)

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(y^2+y))

% output

from above clealy it is the 3rd figure given in the list

so (i) ode represents 3rd figure

(ii):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(y^2-y))

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clearly this figure is 4th in the figure

(iii):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(y^3+y^2))

| 0 -

clearl it none of the figures in the list.

(iv):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(2-t^2))

* 一

it is also none of the figures in the list

(v):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(t*y+t*y^2))

it is also none of the figures in the given list

(vi):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(t^2+t^2*y))

clearly it also none of the figures

(vii):

[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(t+t*y))

(viii):

clear all
[t, y] = meshgrid([-4:0.2:4],[-4:0.2:4]);
grid on
quiver(t,y,ones(size(t)),(t^2-2))

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it is also none of the figures