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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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The correct Answer is:
2
`"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)" "therefore" "log(1+y)=((x^(2)+2x+1))/(2)rArr" "y=e^(((1+x)^(2))/(2))-1`
`"Required answer "=2`
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