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

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 = 9x2 dx y dy

Get the Daily Math Tweet!
IntMath on Twitter