We recognise that we can get it in the form of the second expression at the top of this page.
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
Implicit differentiation gives us:`2x + 2y(dy/dx) = 18x^2`
Multiplying throughout by `dx/2` gives:
`x\ dx + y\ dy = 9x^2dx`
Subtracting y dy gives us our original DE
x dx = 9x2 dx − y dy
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