In this problem we consider an equation in differential form M dx + N dy =...

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In this problem we consider an equation in differential form M dx + N dy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have M₁ - Ñ ₂ = For this exercise we can find an integrating factor which is a function of a alone since Mỹ - N. N can be considered as a function of alone. N = (6x²y³e - 4e¯* sin(x) + 5e¯³) dx + (6x³y²e¯ª – 5€¯¹)dy = 0 Namely we have μµ(x) Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = Which is exact since My = N₂ = = = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) = In this problem we consider an equation in differential form M dx + N dy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have M₁ - Ñ ₂ = For this exercise we can find an integrating factor which is a function of a alone since Mỹ - N. N can be considered as a function of alone. N = (6x²y³e - 4e¯* sin(x) + 5e¯³) dx + (6x³y²e¯ª – 5€¯¹)dy = 0 Namely we have μµ(x) Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = Which is exact since My = N₂ = = = are equal. This 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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