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No. of regular Singular points of the differential equation, x2( x - 2 )2 y" + 2x (x - 2) y’+ (x + 1)y = 0. is __________.
Correct answer is '1'. Can you explain this answer?
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No. of regular Singular points of the differential equation,x2( x - 2 ...
In the normalized form (6,3), this is
Clearly the singular points of the differential equation are x = 0 and x = 2. We investigate them one at a time.
Consider x = 0 first. and form the functions defined by the products
Consider x = 0 first. and form the functions defined by the products
of the form. The product function defined by x2P2(x)f is analytical at x = 0, but that defined by xP1(x) is not. Thus x = 0 is an irregular singular point of Now consider x = 2. Forming the products for this point, we have
Both of the product functions thus defined are analytic at x = 2. and hence x = 2 is a regular singular point.
Most Upvoted Answer
No. of regular Singular points of the differential equation,x2( x - 2 ...
To determine the number of regular singular points of the differential equation, we need to examine the behavior of the equation near the points where the coefficient functions become zero or infinite.
The differential equation is given as x^2(x - 2)^2y.
The coefficient functions are x^2 and (x - 2)^2.
To find the regular singular points, we need to determine the values of x for which these coefficient functions become zero or infinite.
For x^2 = 0, x = 0 is a singular point.
For (x - 2)^2 = 0, x = 2 is a singular point.
Therefore, the differential equation has two regular singular points at x = 0 and x = 2.
The differential equation is given as x^2(x - 2)^2y.
The coefficient functions are x^2 and (x - 2)^2.
To find the regular singular points, we need to determine the values of x for which these coefficient functions become zero or infinite.
For x^2 = 0, x = 0 is a singular point.
For (x - 2)^2 = 0, x = 2 is a singular point.
Therefore, the differential equation has two regular singular points at x = 0 and x = 2.
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No. of regular Singular points of the differential equation,x2( x - 2 )2 y" + 2x (x - 2) y’+ (x + 1)y = 0. is __________.Correct answer is '1'. Can you explain this answer?
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