16.2.7 ca dt, Solve Abel's equation, (t) f(x) = 0

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16 2 7 Ca Dt Solve Abel S Equation T F X 0 A 1 Jo X 1 By The Following Method A Multiply Both Sides By Z 1 (34.87 KiB) Viewed 27 times

16.2.7 ca dt, Solve Abel's equation, (t) f(x) = 0<a<1 Jo (x - 1)" by the following method: (a) Multiply both sides by (z – x)a- and integrate with respect to x over the range 0 sxs z. (b) Reverse the order of integration and evaluate the integral on the right- hand side (with respect to x) by the beta function. Note. dx B(1 - a, a) (z - x)'-(x - 1)" = (-a)!(a - 1)! Die = TL = Sin πα