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(dy)/(dx)=(xy)/((1-x)(1+y)) A) x+y+log[y...

`(dy)/(dx)=(xy)/((1-x)(1+y))` A) `x+y+log[y(1-x)]=c` B) `x+y+log[x(1-y)]=c` C) `x+y+log(x+y)=c` D)`y-x+log[x(1-y)]=c`

A

`x+y+log[y(1-x)]=c`

B

`x+y+log[x(1-y)]=c`

C

`x+y+log(x+y)=c`

D

`y-x+log[x(1-y)]=c`

Text Solution

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A
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Knowledge Check

  • (dy)/(dx)=(1+x)(1+y^(2)) A) (1)/(2)log[(1+y)/(1-y)]=x+(x^(2))/(2)+c B) log(1+y^(2))=x+(x^(2))/(2)+c C) tan^(-1)y=x+(x^(2))/(2)+c D) tan^(-1)x=y+(y^(2))/(2)+c

    A
    `(1)/(2)log[(1+y)/(1-y)]=x+(x^(2))/(2)+c`
    B
    `log(1+y^(2))=x+(x^(2))/(2)+c`
    C
    `tan^(-1)y=x+(x^(2))/(2)+c`
    D
    `tan^(-1)x=y+(y^(2))/(2)+c`

  • (x^(2)-x^(2)y)(dy)/(dx)+y^(2)+x^(2)y^(2)=0 A) x-(x^(-1)+y^(-1))-logy=c B) x+(x^(-1)-y^(-1))=log(cy) C) x^(2)+xy+log((y)/(x))=c D) (x^(-1)-y^(-1))+logy=x+c

    A
    `x-(x^(-1)+y^(-1))-logy=c`
    B
    `x+(x^(-1)-y^(-1))=log(cy)`
    C
    `x^(2)+xy+log((y)/(x))=c`
    D
    `(x^(-1)-y^(-1))+logy=x+c`

  • e^(((1)/(2)(dy)/(dx)))=3^(x) A) y=3^(x)log3+c B) y=x^(2)log3+c C) y=3logx+c D) y=x^(3)log3+c

    A
    `y=3^(x)log3+c`
    B
    `y=x^(2)log3+c`
    C
    `y=3logx+c`
    D
    `y=x^(3)log3+c`

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