If solution of `x^(2)(d^(2)y)/(dx^(2))-9x(dy)/(dx)+21y=0` is of the from `y=c_(1)x^(m)+c_(2)x^(n)(c_(1),c_(2)` are arbitrary constants,`m,n in Z`) then values of m,n can be

If y=(x+sqrt(1+x^(2)))^(n) then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)

The solution of (dy)/(dx) = sqrt(1-x^(2)-y^(2)+x^(2)y^(2)) is Where c is an arbitrary constant.

if x^(m)*y^(n)=1 then (dy)/(dx)

The solution of the differential eqution (d^(2)y)/(dx^(2)) = e^(-2x) is y = c_(1)e^(-2x) +c_(2)x + c_(3) where c_(1) is

The solution of (dy)/(dx) = sqrt(1 - x^(2) -y^(2) + x^(2) y^(2)) is Where c is an arbitrary constant

If x^(m)*y^(n)=(x+y)^(m+n) then (dy)/(dx) is:

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