We recognise that we can get it in the form of the second expression above.

We add y dy to both sides:

x dx + y dy = 9x² dx

Now multiply both sides by 2:

2(x dx + y dy) = 18x² dx

We see that the LHS is in the form of the second expression above. Now integrate both sides:

x² + y² = 6x³ + K

CHECK

Implicit differentiation gives us:

2x + 2y(dy/dx) = 18x²

Dividing through by 2dx'

x dx + y dy = 9x² dx

Subtracting y dy gives us our original DE

x dx = 9x² dx − y dy