Please help me solve this differential equation
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Armel Kapso
am 18 Jul. 2022
Kommentiert: Torsten
am 29 Jul. 2022
please i will like to solve this eqution for w=188 rad/s
Please take a2=3 a3=2, b2=5 and b3=2
3 Kommentare
John D'Errico
am 18 Jul. 2022
You tell us what the value of w is, but not all of the other important parameters. They are just as important. Thus what are a2, a3, b2 b3? If you don't have them, then no numerical solution will be possible. My expectation is no analytical solution will exist in any case, so a numerical solution is your only option.
Akzeptierte Antwort
Sam Chak
am 19 Jul. 2022
Hi @Armel Kapso
Some basic code from the ode45 documentation. Probably looks like this, try manupulating the parameters yourself.
tspan = [0 1]; % simulation time interval
initv = [1 0]; % initial values
[t, x] = ode45(@odefcn, tspan, initv);
plot(t, x(:, 1), 'linewidth', 1.5)
grid on
xlabel({'$t$'}, 'Interpreter', 'latex')
ylabel({'$x(t)$'}, 'Interpreter', 'latex')
title('System Response')
function dxdt = odefcn(t, x)
dxdt = zeros(2, 1);
a2 = 3;
a3 = 2;
b2 = 5;
b3 = 2;
omega = 188;
num = 2*a3*omega^3*sin(x(1) - omega*t)*x(2) + 2*a3*omega*sin(x(1) - omega*t)*x(2)^3 - b3*sin(x(1)) - b3*sin(omega*t);
den = 2*a2 - 2*a3*omega*(2*x(2) + omega)*cos(x(1) - omega*t);
dxdt(1) = x(2);
dxdt(2) = num/den;
end
9 Kommentare
Torsten
am 29 Jul. 2022
Corrected.
a2 = 3;
a3 = 2;
b2 = 5;
b3 = 2;
omega = 210;
f = @(t,x) [x(2);(2*a3*omega^3*sin(x(1)-omega*t)*x(2)+...
2*a3*omega*sin(x(1)-omega*t)*x(2)^3-...
b3*sin(x(1))-b3*sin(omega*t))/(2*a2-2*a3*omega*(2*x(2)+omega)*cos(x(1)-omega*t))];
tspan = linspace(0, 88, 8801);
init = [1 1];
options = odeset('RelTol',1e-8,'AbsTol',1e-8);
[t, x] = ode15s(f, tspan, init, options);
plot(x(:,1), x(:,2))
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Chunru
am 19 Jul. 2022
Bearbeitet: Chunru
am 19 Jul. 2022
opts = odeset('RelTol', 1e-2, 'AbsTol', 1e-4);
[t, x] = ode45(@diffeqn, [0 1], [0.1; .1], opts);
whos
plot(t, x(:,2))
function dxdt = diffeqn(t, x)
a2=3; a3=2; b2=5; b3=2; w=188;
% Check this out
dxdt(1, 1) = x(2);
dxdt(2, 1) = ( (2*a3*w^3*sin(x(2)-w*t))*x(1) + ...
(2*a3*w*sin(x(2)-w*t))*x(1).^3 + ...
(-b2*sin(w*t) - b3*sin(x(2))) ) ./ ...
( 2*a2 -2*a3*w*(2*x(1)+w)*cos(x(2)-w*t) );
end
6 Kommentare
Chunru
am 19 Jul. 2022
You need to save the code in a file, e.g., testdiff.m. Then run the program testdiff.m
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