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The solution of dy/dx (x^(2)y^(3)+xy)=1 ...

The solution of `dy/dx (x^(2)y^(3)+xy)=1 ` is -

A

`1/x = 2 -y^(2) + ce ^(y^(2)/2)`

B

The solution of an equation which is reducible to linear equation

C

`2/x = 1 -y^(2) + e^(-y/2)`

D

`e^(y^(2)/2)((1-2x)/x+y^(2))=c`

Text Solution

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The correct Answer is:
A, B, C
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(x^(2) y^(3) + 2xy) dy = dx

The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is given by

Knowledge Check

  • The solution of dy/dx =(x^(2)+y^(2)+1)/(2xy) satisfying y(1) = 1 is given by -

    A
    a system of hyperbolas
    B
    a system of circles
    C
    `y^(2) = x (1+ x) - 1`
    D
    `(x-2)^(2) + (y - 3)^(2) = 5`

  • The solutions of (dy)/(dx)=(x^(2)+y^(2)+1)/(2xy) satisfying y(1)=1 is given by -

    A
    a system of hyperbola
    B
    a system of circles
    C
    `y^(2)=x(1+x)-1`
    D
    `(x-2)^(2)+(y-3)^(2)=5`

  • The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0 is -

    A
    `tan^(-1)((x)/(y))+log|y|+c=0`
    B
    `2tan^(-1)((x)/(y))+log|x|+c=0`
    C
    `log(y+sqrt(x^(2)+y^(2)))+log|y|+c=0`
    D
    `log(x+sqrt(x^(2)+y^(2)))+log|x|=c`

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