The solution of the differential equatio...

The solution of the differential equation `x=1+x y(dy)/(dx)+(x^2y^2)/(2!)((dy)/d)^2+(x^3y^3)/(3!)((dy)/(dx))^3+ i s` (a) `( b ) (c) y=1n(( d ) x (e))+c (f)` (g) (b) `( h ) (i) (j) y^(( k )2( l ))( m )=( n ) (o)(( p ) (q)1nx (r))^(( s )2( t ))( u )+c (v)` (w) (c) `( d ) (e) y=logx+x y (f)` (g) (d) `( h ) (i) x y=( j ) x^(( k ) y (l))( m )+c (n)` (o)

`y=log_(e)(x)+C`

`y=(log_(e)x)^(2)+C`

`y=pmsqrt((log_(e)x)^(2)+2C)`

`xy=x^(y)+k`

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Verified by Experts

The correct Answer is:

We have,
`x=e^(xy(dy)/(dx))`
`rArr" "logx=xy(dy)/(dx)`
`rArr" "ydy=(logx)/(x)dxrArr" "ydy=logxd(logx)`
On integrating, we get
`(y^(2))/(2)=((logx)^(2))/(2)+C`
`rArr" "y^(2)=(log_(e)x)^(2)+2CrArry=pmsqrt((log_(e)x)^(2)+2C)`

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