# MATH 270 Week 6 iLab Latest

**MATH 270 Week 6 iLab Latest**

Part I: Second Order Homogeneous Differential Equations

1.What is meant by homogeneous? What should you look for to determine the order of a differential equation?

2.Solve the characteristic equation above for the roots . Hint: you may need to solve by factoring or by using the quadratic formula.

4. Write the solution of the differential equation based on the roots found in question 3.

5. Solve the following homogeneous differential equation by repeating the process above.

7. Take the result of question 6 and find the particular solution given that y(0) = 1 and . Why do we need two initial conditions for second order differential equations? How are the initial conditions used to find a particular solution? What must be done in order to use the second initial condition?

Part II: Second Order Non-Homogeneous Differential Equations

1. Follow the six steps below to solve the following:

Remember that the final solution form is

Step 1: Find . This is the homogeneous solution. Use the process outlined in part I above to find it.

Step 5: Solve for the unknown variables A, B, etc. to determine .Hint 1: match like terms on the left and right side. For example, if you had 2A + 3Ax – 5B = 2x + 4, you would set 3Ax = 2x and 2A – 5B = 4. You may have to distribute to clear some parentheses first. Hint 2: You will have to solve a system of equations to find A, B, etc. What are some ways to solve a system of equations?

Step 6: Combine yp and yh to obtain the complete solution