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the solution of the differential equation `(dy)/(dx)+(x(x^(2)+3y^(2))/(y(y^(2)+3x^(2)))=0` isA. `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` |
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Answer» Correct Answer - C 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` |
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