1.2.1. Differential Equation

Try these first

1. 1.

   Define a differential equation.

   Hint

   Think about what makes an equation involve derivatives.

2. 2.

   What is the order of the equation dy/dx = 3x?

   Hint

   Look at the highest derivative present.

3. 3.

   What is a differential equation?

   Hint

   Consider an equation that includes derivatives.

4. 4.

   True or False: All differential equations are linear.

   Hint

   Recall the definition of linear equations.

5. 5.

   Consider the differential equation dy/dx + 4y = e^(2x). Determine the order, degree, and solve it.

   Hint

   Remember the integrating factor method and simplify as needed.

6. 6.

   Given d²y/dx² - 3dy/dx + 2y = 0, solve this second-order homogeneous differential equation.

   Hint

   Identify the auxiliary equation and determine the characteristic roots.