MATLAB: How do you solve 3.5d^2x/dt^2 + 4dx/dt + 5x = 2.5 3e^-2t with matlab

laplaceode

I am trying to solve a differential equation with laplace transform. The equation is

Md^2/dx^2+Cdx/dt+kx=f+f2e^-2t

for t>0. C=4,k=5,f2=3,M=3.5,f=2.5 and initial conditions are x(t=0)=1, dx/dt(t=0)=1

I just do not know how to type this into MATLAB. Please help. Thank you.

Best Answer

 syms x(t)
 C = 4; k = 5; f2 = 3; M = 3.5; f = 2.5
 eqn = M*(diff(x(t), t, t))+C*(diff(x(t), t))+k*x(t) == f+2*f*exp(-2*t);
 sol = dsolve(eqn, x(0) == 1, subs(diff(x(t), t), t, 0) == 1);
 simplify(sol, 'step', 20)

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MATLAB: Please Help Me! i want to plot a equation dx/dt = y-5; dy/dt = -x+5; x(0)=0,y(0)=0. What type of code solver should i use.

   syms x(t) y(t) %EDITED ANSWER
   ode1=diff(x) == y-5;
   ode2=diff(y)== -x+5;
   [x,y]=dsolve(ode1,ode2,x(0)==0,y(0)==0)
   fplot(subs(x),'r')
   hold on 
   fplot(subs(y),'g')

MATLAB: Graphing and finding the closed form solution to a system of differential equations

The following shows how to use the symbolic toolbox to create the handle for the ODEs and then use ode45 to find a numerical solution.

syms t(y) x(y)
dt = diff(t);
ddt = diff(dt);
dx = diff(x);
ddx = diff(dx);
eq1 = ddt == dt^2*(tan(t)) - ddx*4*sec(t);
eq2 = dt^2*(sec(t)-tan(t)) == ddx*sec(t)*(1/0.625-4);
[eqn, vars] = reduceDifferentialOrder([eq1 eq2], [t x]);
[M,F] = massMatrixForm(eqn,vars);
f = M\F;
odeFun = odeFunction(f, vars);
ic = [pi/6; 0; 0; 0];
ode45(odeFun, [0 10], ic)

Alternatively, you can also write your own odeFunction but It require a bit of algebric manipulation

ode = @myodeFun;
t = [0 10];
ic = [pi/6; 0; 0; 0];
[t,y] = ode45(ode, t, ic);
plot(t,y, 'o-');
function dydx = myodeFun(t,x)
    % Rearranged Equations:
    % t'' = -(dt^2*(2*cos(t)*tan(t) - 5))/(3*cos(t))
    % x'' = (5*dt^2*(cos(t)*tan(t) - 1))/12
    % x(1) -> t, x(2) -> t', x(3) -> x, x(4) -> x'
    
    dydx = zeros(4,1);
    dydx(1) = x(2);
    dydx(2) = -(x(2)^2*(2*cos(x(1))*tan(x(1)) - 5))/(3*cos(x(1)));
    dydx(3) = x(4);
    dydx(4) = (5*x(2)^2*(cos(x(1))*tan(x(1)) - 1))/12;
end

Best Answer

Related Solutions

MATLAB: Please Help Me! i want to plot a equation dx/dt = y-5; dy/dt = -x+5; x(0)=0,y(0)=0. What type of code solver should i use.

MATLAB: Graphing and finding the closed form solution to a system of differential equations

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