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How do I use quiver with an implicit differential equation?

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Ramadan M
Ramadan M on 15 Sep 2020
Answered: esat gulhan on 16 Sep 2020
I have pasted the full question below for context, but essentially, I'm having issues ironing out how quiver works for part a. I tried to mimic the example in the textbook, but it returns multiple errors, and I've checked the documentation for quiver, which hasn't helped.
syms y(t)
[T, Y] = meshgrid(-10:0.2:10, -1:0.2:2); %unsure what the bounds should be???
S = (2*y - t)/(2*t - y); %equation
quiver(T, Y, ones(size(S)), S), axis equal tight
xlabel ’t’, ylabel ’y’
title ’Direction Field for dy/dt = (2*y - t)/(2*t - y)’

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Answers (1)

esat gulhan
esat gulhan on 16 Sep 2020
Maybe like this
syms S C c t y
[T, Y] =meshgrid(-10:0.5:10,-10:0.5:10);
S= ((2.*Y-T)./(2.*T-Y))
dT = ones(size(S)); %equation
dyu = S./sqrt(dT.^2+S.^2);
dxu = dT./sqrt(dT.^2+S.^2);
quiver(T,Y,dxu,dyu)
xlabel ’t’, ylabel ’y’
title('Direction Field for dy/dt = (2*y - t)/(2*t - y)')
set(gca, 'XLim', [0 10], 'YLim', [0 10]);
It is not an easy ODE, There is singularity in some fields. Can not be reached with dsolve, can be reach numerically ODE solvers

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