`d/(dx) y^(x)=d/(dx) x^(y)`

Differentiate sin(xy) + (x)/(y) = x^(2) - y

If m, n are order and degree of differential equation y(dy)/(dx) + x^(3)((d^(2)y)/(dx^(2)))-xy = cos x then

Solve the following differential equation : x dx + y d y + (x dy - y dx)/(x^(2) + y^(2))=0

for any differential function y= F (x) : the value of ( d^2 y) /( dx^2) +((dy)/(dx)) ^3 . (d^2 x)/( dy^2)

If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(dx^2)) is equal to P^(x)+P^(prime)(x) (b) P^(x)dotP^(x) P(x)dotP^(x) (d) a constant

The degree of the differential equation (d^(2)y)/(dx^(2))+3((dy)/(dx))^(2)=x^(2)log((d^(2)y)/(dx^(2))), is

The degree of the differential equation (d^(2)y)/(dx^(2))+3((dy)/(dx))^(2)=x^(2)log((d^(2)y)/(dx^(2))), is

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

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

If y=e ^((alpha +1)x) be solution of differential equation (d ^(2)y)/(dx ^(2)) -4 (dy )/(dx) +4y=0, then alpha is: