18.1.1. Ordinary Differential Equation (ODE)

Try these first

1. 1.

   What is the main goal of solving an ODE?

   Hint

   Think about what information is provided in an ODE.

2. 2.

   Define 'Initial Condition'.

   Hint

   Consider how an initial value gives us a starting point.

3. 3.

   What does an ODE involve?

   • Only functions
   • Functions and their derivatives
   • Only derivatives

   Hint

   Consider what is included in the standard form of an ODE.

4. 4.

   True or False: Initial conditions are not necessary for solving ODEs.

   • True
   • False

   Hint

   Think about why we need specific points to solve equations.

5. 5.

   Consider the ODE 𝑦' = -2𝑦 with the initial condition 𝑦(0) = 3. Find the explicit solution for 𝑦.

   Hint

   Recall that this is a first-order linear differential equation; can you solve it using separation of variables or an integrating factor?

6. 6.

   Given the second-order ODE 𝑦'' - 5𝑦' + 6𝑦 = 0, find the general solution.

   Hint

   Consider the characteristic equation formed from the differential equation.