Finding the closed form solution to a system of second order differential equations

4 views (last 30 days)
I am trying to find the closed form solution to a system of differential equations but I am unsure how to access the closed form solutions. How can I modify the code to find the closed form solutions of y and z? Any help would be appreciated.
syms y(t) z(t)
Dy = diff(y,t); %angle
D2y = diff(y,t,2);
Dz = diff(z,t); D2z = diff(z,t,2);
eqns = [-4.905*sin(y)-24.525*sin(y) == 0.046875*D2y + (0.125*sin(y)*(Dy*Dy*cos(y)+D2y*sin(y))) + sin(y)*(D2y*0.625*sin(y))-D2y*cos(y), D2z == Dy*Dy*0.25*sin(y)-D2y*0.25*cos(y)];
fun = matlabFunction(odeToVectorField(eqns),'Vars',{'t','Y','Z'});
tspan = [0 10]; % Time interval for integration
y0 = [pi/3 0 0 0]; % initial conditions
%[t,y] = ode45(fun,tspan,y0);
sol = ode45(fun,[0 20],y0)
fplot(@(x)deval(sol,x,1), [0, 20])

Accepted Answer

Star Strider
Star Strider on 19 Mar 2020
A closed-form solution is likely not possible because both differential equations are nonlinear, specifically:
Most nonlinear differential equations do not have analytic solutions. These are two of them.

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!