The solution of (x^2+x y)dy=(x^2+y^2)dx ...

The solution of `(x^2+x y)dy=(x^2+y^2)dx` is (a) `( b ) (c)logx=log(( d ) (e) x-y (f))+( g ) y/( h ) x (i) (j)+c (k)` (l) (m) `( n ) (o)logx=2log(( p ) (q) x-y (r))+( s ) y/( t ) x (u) (v)+c (w)` (x) (y) `( z ) (aa)logx=log(( b b ) (cc) x-y (dd))+( e e ) x/( f f ) y (gg) (hh)+c (ii)` (jj) (kk) None of these

`logx = log(x-y)+y/x+c`

`logx = 2log(x-y)+y/x+c`

`logx= log(x-y)+x/y+c`

None of these

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The correct Answer is:

`(x^(2)+xy)dy=(x^(2)+y^(2))dx` or `(dy)/(dx) = (x^(2)+y^(2))/(x^(2)+xy)`
Thus, equation reduces to
`x(dv)/(dx) = (1+v^(2))/(1+v) -v=(1+v^(2)-v-v^(2))/(1+v)=(1-v)/(1+v)`
or `-int(1-2/(1-v))dv=int(dx)/x`
or `-v-2log(1-v)=logx+logc`
or `-y/x-2log(x-y)/x=logx+logc`
or `logx=2log(x-y)+y/x+k` where `k=logc`

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CENGAGE ENGLISH-DIFFERENTIAL EQUATIONS-SINGLE CORRECT ANSWER TYPES

x(dy)/(dx)=y(logy-logx+1)
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The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...
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The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...
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The solution of (y+x+5)dy=(y-x+1)dx is (a) ( b ) (c)log(( d ) (e) (f)...
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The slope of the tangent at (x , y) to a curve passing through a po...
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Solutionof the differential equation ydx-xdy+xsqrt(xy)dy=0 is
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The solution of x^(2)(dy)/(dx)-xy=1+cosy/x is
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The solution of the differential equation 2x ^(2)y (dy)/(dx) = tan ( x...
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The solution of the differential equation {1/x-y^(2)/(x-y)^(2)}dx+{x^...
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The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (...
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The curve satisfying the equation (dy)/(dx)=(y(x+y^3))/(x(y^3-x)) and ...
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The solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx)) ...
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The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^...
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The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt...
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