1. Differential Equations MTH 242 Lecture # 08 Dr. Manshoor Ahmed

2. Linear Differential Equations of Higher Order

12. Solution curves of a BVP that pass through two points

13. Linear Differential Equations of Higher Order Example 1 Consider the function We can prove that this function is a solution of the boundary-value problem Since, Therefore,

14. Linear Differential Equations of Higher Order

16. Also, When Implies Since, for any choice of ‘c’ it follows that for the problem The solution is the one parameter family

17. Linear Dependence and Linear Independence

25. Example 1 Let ‘a’ and ‘B’ are real numbers and then, and are linearly independent on any interval of the x-axis since So functions are linearly independent.

26. Linear Dependence and Linear Independence

28. Summary Higher order linear differential equation. Homogeneous and non-homogeneous equations with constant coefficients. Initial value problem (IVP) and it’s solution. Existence and Uniqueness of Solutions. Boundary value problem (BVP) and it’s solution. Linear independence and dependence of functions. Wronskian of a set of functions.