Transcribed Image Text: In ts problem we consider an equation in differential form M dx + N dy = 0. The

Excerpt
M dx + N dy = 0 where M = N = Wch is exact since M, = N = are equal. Ts problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) =

Transcribed Image Text: In ts problem we consider an equation in differential form M dx + N dy = 0.
The equation
(6x + 4x’y2) dx + (6x² – + 3)dy = 0
y
in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have
M, – N, =
For ts exercise we can find an integrating factor wch is a function of y alone since
M,- N,
M
is a function of y alone.
Namely we have u(y) =|
Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where
M =
N =
Wch is exact since
M, =
N =
are equal.
Ts problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where
F(x, y) =

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