If the solution of the differential equation `(1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0` is `x+kye^((x)/(y))=C` (where, C is an arbitrary constant), then the value of k is equal to

If the solution of the differential equation y^(3)x^(2)cos(x^(3))dx+sin(x^(3))y^(2)dy=(x)/(3)dx is 2sin(x^(3))y^(k)=x^(2)+C (where C is an arbitrary constant), then the value of k is equal to

If the solution of the differential equation y^(3)x^(2)cos(x^(3))dx+sin(x^(3))y^(2)dy=(x)/(3)dx is 2sin(x^(3))y^(k)=x^(2)+C (where C is an arbitrary constant), then the value of k is equal to

Solution of the differential equation (x-y)(1-(dy)/(dx))=e^(x) is

The solution of the differential equation (dy)/(dx)=(xy+y)/(xy+x) is y-lambda x=ln((x)/(y))+C (where, C is an arbitrary constant and x, y gt0 ). Then, the valeu of lambda is equal to

The solution of the differential equation (dy)/(dx)=(xy+y)/(xy+x) is y-lambda x=ln((x)/(y))+C (where, C is an arbitrary constant and x, y gt0 ). Then, the valeu of lambda is equal to

The solution of the differential equation (1+e^(x))y(dy)/(dx) = e^(x) when y=1 and x = 0 is

The solution of the differential equation (dy)/(dx)=e^(y)(1/(2x^2)+1), (AA x gt0) is lambdaxe^(-y)=1-2x^(2) (where c is an arbitrary constant). Then, the value of lambda is equal to

The solution of the differential equation x(e^(2y)-1)dy+(x^2-1)e^y dx=0 is

The solution of the differential equation x(e^(2y)-1)dy + (x^2-1) e^y dx=0 is