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

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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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