1.3. First-Order Linear Differential Equations

Try these first

1. 1.

   What is the general form of a first-order linear differential equation?

   Hint

   Look for the highest derivative.

2. 2.

   What does the variable P(x) represent in this equation?

   Hint

   Think about how y is influenced.

3. 3.

   What is a first-order linear differential equation?

   • dy/dx + P(y) = Q(x)
   • dy/dx + P(x)y = Q(x)
   • d^2y/dx^2 + P(x)y = Q(x)

   Hint

   Look for the derivative order.

4. 4.

   The integrating factor µ(x) is defined as e^(∫P(x)dx). Is this statement True or False?

   • True
   • False

   Hint

   What is the purpose of the integrating factor again?

5. 5.

   Given dy/dx + 4y = sin(x), find y.

   Hint

   Use the integrating factor, then go to the integration step.

6. 6.

   Explain how the solution changes if Q(x) is non-linear. Provide an example.

   Hint

   Consider the nature of the equation based on Q(x).