Question

I'm trying to solve this differential equations by using matlab. But I don't know the reason why I can't get the solutions. I've attached matlab code and few differential equation. Please find a the way to solve this problem.

second oder ode2.m x+ function, second-oder-ode2 t-0:0.001:30 initial-x = 0; initial-dxdt = 0: lt.影=ode45( @rhs, t, [initial.x initial.dxdt ] ); plot(t.(:,1l): xlabel( t); ylabel(x): 申 function dxdt=rhs( t, x) dxdt-1 =x(2); dxdt-2 (-50 x(2)+61.25+((1-cos(4 pi 10 t))/2) (47380 x(1)-3-7428 x(1) 2 366*x(1)-7)): end end 오후 10.1 닛 れな. -56 166

Answer 1

Matlab code

function second_order_ode2
t=0:0.001:30;
initial_x=0;
initial_dxdt=0;
[t,x]=ode45(@rhs,t,[initial_x initial_dxdt]);
plot(t,x(:,1))
xlabel('t')
ylabel('x')
function dxdt=rhs(t,x)
dxdt_1=x(2);
dxdt_2=(-50*x(2)+61.25+((1-cos(4*pi*10*t))/2).*(47380*x(1).^3-7428*x(1).^2+366*x(1)-7));
dxdt=[dxdt_1;dxdt_2];
end
end

Output

18 16 14 12 10 6 4 2 0 0.3 0.05 0.15 0.2 0.25

Warning: Failure at t=2.606178e-01. Unable to meet integration tolerances without reducing the step size below the smallest
value allowed (8.881784e-16) at time t.

This ODE is most likely encountering a singularity.that could i see at least,maybe piecewise integration will do..but finding the singularity the hard part,and Matlab has difficulty to find it