verify that ϱ^x and x are the solution of the homogeneous equation corresponding to (1−x)y^2 +xy^1 −y=2(x−1)^2 ϱ^(x ) , 0<x<1 and find the general solution.


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Question Number 133403 by Engr_Jidda last updated on 21/Feb/21

$v e r i f y t h a t ϱ^{x} a n d x a r e t h e s o l u t i o n$ $o f t h e h o m o g e n e o u s e q u a t i o n c o r r e s p o n d i n g$ $t o (1 - x) y^{2} + {x y}^{1} - y = 2 {(x - 1)}^{2} ϱ^{x}, 0 < x < 1$ $a n d f i n d t h e g e n e r a l s o l u t i o n .$
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