Is it allowed to use the quadratic solution formula for a differential equation

Question

I have some trouble with a challenging fluid mechanics problem. The problem leads me to a non-linear ode 1st order.

$0={\dot p_C}^2+\frac{k_1}{k_2 C}\dot p_C+\frac{p_C-p_0}{k_2C^2}$

My Idea was now to change the equation to $\dot p_C$ and solve this in Simulink. So I used the quadratic solution formula.

$0=x^2+px+q \to x_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p^2}{4}-q}$

Now I'm not sure. Am I allowed to do that at this differential equation?

Some first simulations show, that my approach get some good looking results — Erik Sommer, Jun 22 '13 at 13:23

score 0 · Answer 1 · answered Sep 23 '13 at 13:14

0

Sure, as long as you actually want to find the x-intercepts of the differentiated equation, or rather turning points of the original equation

answered Sep 23 '13 at 13:14

Wilhelm Erasmus

1 Answers1