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If (x-y)e^ x/x-y =a,prove that y …

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If (x-y)e^ x/x-y =a,prove that y dy/dx+x =2y

Posted by Srivinayak V 6 years, 9 months ago

CBSE > Class 12 > Mathematics

1 answers

Aisha Gupta 6 years, 9 months ago

(X-Y)e^x/x-y=a ->e^x/x-y=a/x-y Taking log both side we have. Log(e^x/x-y)=Loga/x-y ->x/x-y=loga-log(x-y) Now diff both side w.r.t x x-y-(1-dy/dx)x/(x-y)²=dy/dx-1/(x-y) ->-y+xdy/dx=(x-y)(dy/dx-1) ->-y+xdy/dx=xdy/dx-ydy/dx-x+y ->-y+ydy/dx+x=y ->ydy/dx+x=2y

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