The solution of the DE ` (e ^(x) + 1) y dy= ( y + 1) e ^(x) dx` isA. ` e ^(y) = C (e ^(x) + 1) ( y + 1 )`B. `e^(y)= e ^(x) + y + 1 `C. ` y = (e ^(x) + 1 ) ( y + 1)`D. none of these

The solution of the DE ` (e ^(x) + 1) y dy= ( y + 1) e ^(x) dx` isA. `

1.	The solution of the DE ` (e ^(x) + 1) y dy= ( y + 1) e ^(x) dx` isA. ` e ^(y) = C (e ^(x) + 1) ( y + 1 )`B. `e^(y)= e ^(x) + y + 1 `C. ` y = (e ^(x) + 1 ) ( y + 1)`D. none of these
Answer» Correct Answer - A `int ( e ^(x)) /(( e ^(x) + 1 )) dx = int (( y )/( y + 1 )) dy rArr log ( e ^(x) + 1 ) = int (1 - (1)/( y + 1 )) dy ` `rArr y - log ( y + 1 ) = log ( e ^(x) + 1 ) + log C rArr y = log [C( e ^(x) + 1 ) ( y + 1) ]` ` rArr e ^(y) = C ( e ^(x) + 1) ( y + 1 )`