I would like to solve a problem of the type(adsbygoogle = window.adsbygoogle || []).push({});

(da/dt)^2 + f(a)* (da/dt) = g(a) (1)

a=a(t) unknown function

f(a), g(a) = known functions of a.

This differential equation is a first order ODE but (da/dt)^2 makes it different compared to a typical first order ODEs (at least to my knowledge)

I would like to find a(t) satisfying (1) subject to certain initial conditions (say a(0.1)=2).

I feel that no appropriate analytical solution exists for this type of problem, so I am looking for a numerical method to integrate it.

I am thinking of setting da/dt=y thus having

---------------------------

y^2 + f(a)* y = g(a)

da/dt=y

----------------------------

and then writing da/dt = ( a(i+1) - a(i) ) /dt

so the problem becomes

---------------------------

y^2 + f(a(i))* y = g(a(i)) (2)

a(i+1) = dt*y + a(i) (3)

----------------------------

Now I am thinking of solving (2) for the value of y which corresponds at i=0 and then keep one the two solutions (which one to keep is not very clear ….(or if they are both imaginaray?)) Then with a selected small dt (say dt=0.001) find a(i+1). Then continue the iteration scheme this way.

I know a priori that da/dt is positive and thus a(t) is an increasing function of t.

I would like to have opinion from you whether the previous reasoning is TOTALLY WRONG or not. If it wrong I would appreciate if you just give a hint of how to attack the problem

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# First order ode question

**Physics Forums | Science Articles, Homework Help, Discussion**