1. Differential Equation
Chapter 4
Non Homogeneous
Differential Equation
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Method of Variation of Parameters Chapter 4

2. Method of Variation of Parameters Chapter 4
The general solution of the non - homogeneous differential equation
There are two parts of the solution:
solution of the homogeneous part of DE
particular solution
General Solution
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Method of Variation of Parameters Chapter 4

3. Method of Variation of Parameters Chapter 4
General solution
Particular Solution
Complementary Function, solution of Homgeneous part
Due to f(x)
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Method of Variation of Parameters Chapter 4

4. Method of Variation of Parameters Chapter 4
This method can be applied to any non-homogeneous differential equation no matter
What the coefficients and the function f(x) are.
Method of undetermined coefficients is mostly quicker and easier to apply as it involves differentiation. Whereas method of variation of parameters involve
Integration. We may prefer to use method of undetermined coefficients where ever possible.
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Method of Variation of Parameters Chapter 4

5. Method of Variation of Parameters Chapter 4
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Method of Variation of Parameters Chapter 4

6. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4

7. Method of Variation of Parameters Chapter 4
To apply method of variation of parameters
STEP: 1.
Step:2. Identify
Step:3.
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Method of Variation of Parameters Chapter 4

8. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4

9. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4

10. Method of Variation of Parameters Chapter 4
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Method of Variation of Parameters Chapter 4

11. Method of Variation of Parameters Chapter 4
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Method of Variation of Parameters Chapter 4

12. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4

13. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4

14. Method of Variation of Parameters Chapter 4
4/14/2017
Method of Variation of Parameters Chapter 4