prakash ki kirne kanch ke slab per aapartit hone per bartan ke paschat saat rango main kyon vibhakt nahin hota
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On dividing the given equation by x^2, it becomes y'' - 2[(1+x)/x]y' + 2(1+x)y/x^2 = x, which is a second order linear differential equation of the form : y''+f(x)y'+g(x)y = r(x), where x.f(x) and (x^2).g((x) and r(x) are analytic at x=0, i.e. x=0, is a regular singular point of the equation. Accordingly we apply the Frobenius' Extended Power series method and put
y=Sigma(n=0 to inf.)(c_n)x^(n+k), in the original equation, where the coefficients c_n and the index k are to be determined by differentiating the above, twice with respect to x and by comparison of coefficients of x on the two sides of the equation.
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Jayesh BigRedMaths, Mathematics Teacher at Big Red Maths (2018-present)
Answered May 28, 2020
Answer:
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Explanation:
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