Numerically Solving non-linear differential equation

I want to solve the following ode numerically:

with initial conditions and time span as needed.

[Jan]

Okay. What is your question? What have you tried so far and what is your problem?

An ODE must define the deriviative of the function for a specific point and time uniquely.

[James Tursa]

is this really dy/dt raised to the 4th power as you have written? Or is it really supposed to be the 4th derivative of y? Same question for the squared term. What physical system does this represent?

[John D'Errico]

I'd suggest before people run in at full tilt to solve the problem, that you get some confirmation as to the real ODE. Is this a 4th order ODE, or is that the 4th power of the first derivative?

Answer 1

[Alan Stevens]

I guess you could treat the equation as a quadratic in (dy/dt)^2, solve for that, then take the square root to get an expression for dy/dt in terms of y. You could then define the function

dydt = @(t,y) sqrt((-1+sqrt(1+4/y))/2); 

and use ode45 to solve it, once you have set an initial value for y and a time span.