We’re taking very basic differential equations in school and I know how to solve them (more or less) but I think I’d be better when I u derstand what this is doing. Like we use differentiation to find the slope of a curve integration to find the curve equation from a given slope of a point or find the area under the curve
When I solve a differential equation. What is it that I do?
In: Mathematics
You are looking at this wrong.
Dif Eq is about how to use and solve for differentials in algebraic-like equations. You learn to solve the dif eq for any component of the dif eq.
Dif Eqs are used extensuvely to model complex physical systems. A good example…a car is driving down a hill. The driver pushes the gas pedal to the floor. What happens?
Note that the question is very open ended and general. This is a real question for the real world.
To answer the question, you have to build a dif eq.
The components:
1. The velocity, which is derivative of position.
2. The acceleration of the car based on gravity.
3. The acceleration of the car based on the engine power and the weight of the car. The weight of the car depends, in part, on how fast the fuel is consumed by the car.
4. The wind resistance, which is based on the velocity of the car and the air density.
5. The air density is based on the altitude of the car, which is based on the slope of the hill and the velocity of the car.
And on and on and on…you can go further down the rabbit hole.
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