The solution of the differential equation `(dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0` is (a)`x^(4)+y^(4)+x^(2)y^(2)=c` (b)`x^(4)+y^(4)+3x^(2)y^(2)=c` (c)`x^(4)+y^(4)+6x^(2)y^(2)=c` (d)`x^(4)+y^(4)+9x^(2)y^(2)=c`

Options

A. `x^(4)+y^(4)+x^(2)y^(2)=c`
B. `x^(4)+y^(4)+3x^(2)y^(2)=c`
C. `x^(4)+y^(4)+6x^(2)y^(2)=c`
D. `x^(4)+y^(4)+9x^(2)y^(2)=c`

Answer

C

Explanation

put `y=vx`
Differential equal becomes
`int(4(v^(3)+3v))/(v^(4)+6v^(2)+1)dv=-4int(dx)/(x)`
`ln(v^(4)+6v^(2)+1)=-4lnx+lnc`
`impliesx^(4)+y^(4)+6x^(2)y^(2)=c`