Find the differential equation of all circles x² +y² + 2gx = 0 which pass through the origin and whose centres are on the X-axis.

Form the differential equation for \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \)=1 where a & b are arbitrary constants.

Form the differential equation for y = (A + Bx)e^3x where A and B are constants.

Solve: sec 2x dy - sin 5x sec² y dx = 0

Solve: cos²x dy + y.e^tanx dx = 0