Can a Nonlinear DE with Constant Coefficients be Solved Analytically?

[mike79]

dear friends,
i need to solve analitically(also by means of approximate methods) the following nonlinear differential equation:
(A+BTs^(3))*dTs/dt+C*Ts^(4)=D

where Ts is a function of t. A, B, C and D are costants. the initial condition is Ts(0)=Ti.
I would be so grateful if anyone can help me.

Regards
Michele

 

[DavidWhitbeck]

You need to show your work first, that's how it works on this forum.

I will give you a hint anyway-- you can solve it using a technique you learned in calculus! It's that simple (that gave it away since you probably only learned that one method to solve de's when you were in calc).

 

[mike79]

the mentioned equation is the result of the integration of the heat diffusion eqaution following the approximate integral method. is it possible to use any methods to linearize this equation?

 

[Defennder]

As DavidWhitBeck said, you don't have to resort to any fancy numerical methods at all. You're given a differential equation for which 't' does not appear at all, only Ts(t). What does that tell you about how to solve it?