Determine whether the given differential equation is exact. if it is exact, solve it. (if it is not exact, enter not.) (3x + 6y)
dx + (6x − 8y3) dy = 0
1 answer:
The ODE is exact if
. We have
so the equation is indeed exact.
We're looking for a solution of the form
By the chain rule, we have
which means
and
.
Now
Differentiating with respect to
yields
and so the general solution is
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