ode45 third order ode

how to solve

f''' = { [3 * f' * (f'')^2] / [(f')^2 + 1]^(5/2) + 1/f^3 - 1/f^2 + 3} * { [(f')^2 + 1]^(3/2) }

using ode45

with

f(0) = 1.1

f'(0) = 17.1

f''(0) = 144.1

Answer 1

[Ameer Hamza]

Use ode45(). this ODE can be written as a system of 3 first-order ODEs

odeFun = @(t, y) [y(2);
                  y(3);
                  ((3*y(2).*y(3).^2)./(y(2).^2 + 1).^(5/2) + 1./y(1).^3 - 1/y(1).^2 + 3).*((y(2).^2 + 1).^(3/2))];
              
tspan = [0 1];
ic = [1.1; 17.1; 144.1];
[t, y] = ode45(odeFun, tspan, ic);
plot(t, y);

However, it seems that the ODE is unstable, and the solution diverges to infinity. You may check if the equation is written correctly.