Chapter 9 – Differential Equations

1. Define the order of a differential equation.

2. What is the degree of a differential equation?

3. Find the order of d²y/dx² + dy/dx = x.

4. Is y=Ceˣ a family of curves?

5. Write the general form of a first-order linear differential equation.

6. What is meant by a solution of a differential equation?

1. Solve dy/dx=2x.

2. Solve dy/dx=y.

3. Form a differential equation representing y=aeˣ.

1. Solve dy/dx + y = eˣ using the integrating-factor method.

2. Solve dy/dx = (1+x²)/(1+y²).

3. Find the particular solution of dy/dx=3x² given y=2 when x=1.

1. Find the differential equation of the family y=Aeˣ+Be⁻ˣ. Eliminate the arbitrary constants and obtain a second-order differential equation.