The general solution of the DE ` ( y - x ) dy + (x + y ) dx = 0 ` isA. ` tan ^(-1)""(y)/(x) = C sqrt (x ^(2) + y ^(2))`B. ` e ^(tan ^(-1) ( y//x)) = C sqrt (x ^(2) + y ^(2))`C. `tan ^(-1) ((y)/(x))= x ^(2) + y ^(2) + C `D. none of these

The general solution of the DE ` ( y - x ) dy + (x + y ) dx = 0 ` isA.

1.	The general solution of the DE ` ( y - x ) dy + (x + y ) dx = 0 ` isA. ` tan ^(-1)""(y)/(x) = C sqrt (x ^(2) + y ^(2))`B. ` e ^(tan ^(-1) ( y//x)) = C sqrt (x ^(2) + y ^(2))`C. `tan ^(-1) ((y)/(x))= x ^(2) + y ^(2) + C `D. none of these
Answer» Correct Answer - B ` (dy)/(dx) = ( x+ y )/( x - y ) `, which is clearly homogeneous. Put ` y= vx and (dy)/(dx) = v + x ( dv )/(dx) rArr int ((1 - v ))/(( 1+ v ^(2))) dv = int (1)/(x) dx ` `rArr int (dv)/((1 + v ^(2))) - (1)/(2) int (2v)/((1+ v^(2))) dv = int (1)/(x) dx ` `rArr tan ^(-1) v - (1)/(2) log (1 + v ^(2)) = log x + log C rArr tan ^(-1) v = log (Cx sqrt (1 + v ^(2)))` ` rArr tan ^(-1) "" ( y )/(x) = log (C sqrt ( x ^(2) + y ^(2))) rArr e ^( tan ^(-1) y//x) = C sqrt (x ^(2) + y ^(2))`.