If y = A/x be the solution of the value 6ydx + 6xdy = 0 under y(- 1) = 1 then value of A is
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1 thought on “If y = A/x be the solution of the value 6ydx + 6xdy = 0 under y(- 1) = 1 then value of A is<br />​”

1. Answer:

   Answer

   3

   xdy=ydx+y

   2

   dy

   −y

   2

   dy=ydx+y

   2

   dy

   dy=

   −y

   2

   ydx−xdy

   (usiny formula

   −y

   2

   ydx−xdy

   =d(

   y

   x

   ))

   dy=−(d(

   y

   x

   ))

   Integrating both side worot x

   ⇒y=

   y

   −x

   +c

   1

   now,

   y(I)=1Ifx=1,y=1

   ⇒I=

   I

   −1

   +c

   1

   c

   1

   =2

   y=

   y

   −x

   +2

   Ifx=−3

   ⇒y=

   y

   +3

   +2

   ⇒y

   2

   −2y−3=0

   ⇒y

   2

   −3y+y−3=0

   ⇒y(y−3)+1(y−3)=0

   ⇒(y−3)(y+1)=0

   y=3,−1

   Hence,

   y=3

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