The general solution of the DE ` (dy)/(dx) = ( y^(2)- x ^(2))/( 2xy )` isA. ` x ^(2) - y ^(2) = C _1 x `B. `x ^(2) + y ^(2) = C_1 y `C. `x ^(2) + y ^(2) = C_1 x `D. none of these

The general solution of the DE ` (dy)/(dx) = ( y^(2)- x ^(2))/( 2xy )`

1.	The general solution of the DE ` (dy)/(dx) = ( y^(2)- x ^(2))/( 2xy )` isA. ` x ^(2) - y ^(2) = C _1 x `B. `x ^(2) + y ^(2) = C_1 y `C. `x ^(2) + y ^(2) = C_1 x `D. none of these
Answer» Correct Answer - C The given De is homogeneous. Put `y = v x and (dy)/(dx) = v + x (dv)/(dx) `. ` therefore int ( 2v)/( ( 1+ v ^(2))) dv = - int (1)/(x) dx rArr log ( 1 + v ^(2) ) + log x = log C ` ` therefore x ^(2) + y^(2) = C_1 x`.