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**Unformatted text preview: **(3 x 2 y 2 + 4 e y + 2) + (2 x 3 y + 4 xe y-9 y 2 ) y = 0 is exact and ﬁnd the solution. Sometimes a diﬀerential equation is not exact but becomes exact when you multiply by some function μ ( x,y ). Then μ ( x,y ) is called an integrating factor . There are various tricks that sometimes work to produce integrating factors, e.g., Problems 23 and 24 on page 100, but we will be satisﬁed with knowing what integrating factors are and what they are good for. EXAMPLE. Show that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation. " 3 x + 6 y # dx + " x 2 y + 3 y x # dy = 0 , μ ( x,y ) = xy HOMEWORK: SECTION 2.6...

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