If Y Log 1 Cos 2 X1 E 2x Show That Dydx E 2x 1 E 2x Sinxcosx 1 Cos 2 X Let y =(log x) x x log x Also, let u =(log x) x and v = x log x ∴ y = u v `⇒"dy"/"dx" = "du"/"dx""dv"/"dx"` (1) u = (logx) x ⇒ log u = log(log x) xDifferential Equations 1 Quiz 5 Solutions For each of the following differential equations, finding an integrating factor and verify (a) ( 2 x 2 y ) dx ( x 2 y x ) dy = 0 (b) 2 x y dx ( y 2 x 2) dy = 0 (c) ( y 2 x y 1 ) dx ( x 2 x y 1 ) dy = 0With M = y 2 x y 1 and N = x 2 x y 1, note that ( N x M y) / ( x M y N ) = ( x y ) / ( x ( y 2 x y 1 ) y ( x Y=log(1-x^2/1 x^2) find dy/dx