if (x-y) ex/x-y = a ,prove that ydy/dx + x = 2y - Maths - Continuity and Differentiability

Question

if (x-y) ex/x-y = a ,prove that ydy/dx + x = 2y

Rupak Bhattacharya · Accepted Answer

We have,x-y
 exx-y = aTaking logarithm both sides, we getlogx-y
 exx-y = log a⇒log x-y + logexx-y = log a⇒logx-y + xx-y = log adifferentiating both sides, wrt 'x', we get    1x-y1-dydx + x-y×1 - x1 - dydxx-y2 = 0⇒1 - dydx + 1x-yxdydx - y = 0⇒xx-y - 1dydx = yx-y - 1⇒x-x+yx-ydydx = y-x+yx-y⇒ydydx = 2y - x⇒ydydx + x = 2y

if (x-y).ex/x-y = a ,prove that ydy/dx + x = 2y

if (x-y).e^x/x-y= a ,prove that ydy/dx + x = 2y