Infinite series method
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The following second order Differential Equations must be solved with the appropriate Infinite Series Method. You may verify DE with other method only after work is shown step by step using the infinite series methods.
Problems
Use appropriate infinite series method about x=0 to find solutions of the given DE.
1) xy"-(x+2)y'+2y=0
2) (cosx)y"+y=0
Please show all work step by step
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Solution Summary
This shows how to use infinite series to solve second order differential equations.
Solution Preview
Please see the attached file.
1) xy"-(x+2)y'+2y=0.....(1)
Solution:
Write the given equation as
Comparing it with , we get
Since xP(x) and x2Q(x) are both analytic at x=0, so x=0 is a regular singular point of (1).
Let the series solution of (1) be,
...(2)
Substituting these values in (1), we get
...(4), which is an identity.
Making the coefficient ...
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