Form the differential equation by eliminating the arbitrary constants A and B from y = A cos x + B sin x.

Find the differential equation of the family of circles passing through the points (a, 0) and (−a, 0).

Find the differential equation of the family of all ellipses having foci on the x -axis and centre at the origin.

Find the particular solution of (1+ x³)dy − x² ydx = 0 satisfying the condition y(1) = 2.

Solve y' = sin² (x − y + 1 ).

Solve : \(\frac { dy }{ dx } =\sqrt { 4x+2y-1 } \)

Solve \(\frac { dy }{ dx } =\frac { x-y+5 }{ 2(x-y)+7 } .\)

Solve [y(1-x tan x)+x² cosx] dx-dy = 0

Solve (1+x³)\(\frac { dy }{ dx } \)+ 6x²y = 1+x².

Solve ye^ydx = (y³+2xe^y)dy