# Creating a path with differential equations

I'm currently trying to create a 3-D vector field based on an equation. Once I create a vector field, how to actually make the object move along the vector field when placed at a point?

My Approach: Every vector field has an associated system of differential equations. For example, for a vector field, $$\vec A = x \hat{i}+y \hat{j}+z \hat{k}$$ the associated system differential equations are, $$\frac{dx}{dt}=x \\ \frac{dy}{dt} = y\\ \frac{dz}{dt}=z$$ and the corresponding solutions are $$x(t)=x_0 e^t\\ y(t)=y_0e^t \\ z(t)=z_0e^t$$

So now, we have path(i.e.) by varying t, we obtain a set of $$(x,y,z)$$.

Is there a way to solve this system of ODEs with blender. I found an answer, that was relevant, Can you animate objects using differential equations?, but I couldn't understand how to implement all those in this context.

• Thank you for answering. I just gave an example, for a field. In general, $\vec A= P \hat{i} + Q \hat{j} + R \hat{k}$ the corresponding equations are, $\dfrac{dx}{dt}=P, \, \dfrac{dy}{dt} = Q,\, \dfrac{dz}{dt}=R$ for which I don't know the solutions. – Aravindh Vasu Oct 31 '19 at 17:06