How are differential equations used for modeling natural phenomena?

Answer 1

It’s all about balancing an equation so like in physics you have velocity which in DE terms is the first derivative

if you recall a physic equation

x=1/2at^2+v_0t+x_0 this is actually a second order ODE

x=1/2d^2x/dt^2*t^2+dx/dt*t+x_0

there are many ways to build an equation like if you were considering a room with temperature changing at different locations in the room, you could add everything together in and equation as long as it’s balanced e.g. the sun of force must be zero in a system, so using that kind of logic.