If the solution of the differential equation `y=2px+y^(2)p^(k)` is in the form `y^(2)=2cx+c' ` then `k=` (where `p=(dy)/(dx)` and `c` is arbitrary constant)

The solution of the differential equation (x+2y^(2))(dy)/(dx)=y , is

Form the differential equation of y=px+(p)/(sqrt(1+p^(2).

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

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 (dy)/(dx)=(x^(3)+xy^(2))/(y^(3)-yx^(2)) is y^(k)-x^(k)=2x^(2)y^(2)+lambda (where, lambda is an arbitrary constant), then the value of k is

The solution of the differential equation (dy)/(dx)=(2x-y)/(x-6y) is (where c is an arbitrary constant)

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

The solution of the differential equation (dy)/(dx)=(x-y)/(x+4y) is (where C is the constant of integration)