How to solve higher order nonlinear ode in matlab?

I want to solve non linear higher order ode

6u_x^2+6uu_xx+12uu_x^2+6u^2 u_xx+u_xxxx+a^2 u_xx=0;

where a is constant not equal to zero.

There is no initial value given.

[Ameer Hamza]

The notation is not clear. Can you attack the equation in latex format?

[priya anjali]

where a is constant not equal to zero.

[priya anjali]

I made the following system of nonlinear odes:

[Ameer Hamza]

Is the value of 'a' known or unknown? Are you trying to find a numerical solution or a symbolic solution?

[priya anjali]

It's unknown not equal to zero, both numerical and symbolic.

Answer 1

[Ameer Hamza]

You need to convert the higher-order (say n-th order) ODE equation into a system of n first-order ODE equations. See this example: https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uj8b