10.1.2. Prerequisites

Try these first

1. 1.

   What is the general form of a first-order ODE?

   Hint

   Think about how y changes with respect to x.

2. 2.

   Define what Initial Value Problem (IVP) means.

   Hint

   What does the problem require to start solving?

3. 3.

   What is the general form of a first-order ODE?

   • dy/dx = f(x
   • y)
   • dy/dx = f(y)
   • dy/dx = x

   Hint

   Consider what both variables represent in the equation.

4. 4.

   Is an Initial Value Problem (IVP) advanced to solve without initial conditions?

   • True
   • False

   Hint

   What happens when you do not start with a specific point?

5. 5.

   Create a first-order ODE from a real-world scenario, including an initial condition, and explain why the scenario is appropriately modeled by that ODE.

   Hint

   Think about a situation where everything has a rate of change.

6. 6.

   Analyze how changing the step size affects the solution accuracy for a given IVP, using a specific example.

   Hint

   Run simulations with different sizes and compare the outcomes.