1.3.2. Solution Method: Integrating Factor (IF)

Try these first

1. 1.

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

   Hint

   Look for the terms dy/dx and the functions of x.

2. 2.

   Define an Integrating Factor.

   Hint

   Think about how it helps in integration.

3. 3.

   What is the purpose of the Integrating Factor in differential equations?

   • To multiply the dependent variable
   • To simplify the equation for integration
   • To find the derivative directly

   Hint

   Think about what happens when we apply it to the left side of the equation.

4. 4.

   True or False: The Integrating Factor is always e^(∫P(x)dx).

   • True
   • False

   Hint

   Recall the formula we discussed for calculating the Integrating Factor.

5. 5.

   Solve the differential equation dy/dx + 2y = sin(x).

   Hint

   Focus on integrating the right side after applying the Integrating Factor.

6. 6.

   A tank fills with water at a rate described by dy/dt + 0.5y = 10. Find y(t).

   Hint

   Use the Integrating Factor and initial conditions to simplify and solve.