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if ( dy )/(dx) =1 + x +y +xy and y ( -1)...

if `( dy )/(dx) =1 + x +y +xy` and `y ( -1) =0 `, then the value of `( y (0) +3 - e^(1//2))`

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Given, `( dy )/( dx) = ( 1+ x ) ( 1+ y ) rArr ( 1)/( 1_ y ) dy = ( 1+ x ) dx rArr log ( 1+y) = x+ ( x^(2))/( 2) + c ` At `y ( -1) = 0 rArr c = ( 1)/( 2) :. log ( 1+y ) = ( ( x^(2)+ 2x + 1 ) )/(2) rArr y = e^(((1+x)^(2))/(2)) -1`
Required answer = 2
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