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= 9x^{2}dx

Now multiply both sides by 2:

2(

x dx+y dy) = 18x^{2}dx

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

x^{2}+y^{2}= 6x^{3}+K

**CHECK**

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 *= 9*x*^{2} *dx* − * **y* *dy*

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