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Unformatted text preview: x + h ( y ) ψ y = ∂ψ ∂y = x + h ( y ) Comparing this to: N =4 y + x h ( y ) =4 y ⇒ h ( y ) = 2 y 2 + C The ﬁnal answer becomes: 3 x 3 + xyx2 y 2 = C 16.) ( ye 2 xy + x )d x + ( bxe 2 xy )d y = 0 ∂M ∂y = ∂ ( ye 2 xy ) ∂y = e 2 xy + 2 xye 2 xy ∂N ∂x = ∂ ( bxe 2 xy ) ∂y = be 2 xy + 2 bxye 2 xy Equation is exact if b = 1. Using M to solve (and integrating by parts): ψ = Z M d x = Z ( ye 2 xy + x )d x = 1 2 e 2 xy + 1 2 x 2 + h ( y ) ψ y = ∂ψ ∂y = xe 2 xy + h ( y ) Comparing this to: N = xe 2 xy h ( y ) = 0 ⇒ h ( y ) = C 3 The answer becomes: 1 2 e 2 xy + 1 2 x 2 = C We can also multiply both sides by 2 and change 2 C → C to get the answer in the form: e 2 xy + x 2 = C 4...
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 Spring '07
 TERRELL,R
 Math, Trigraph, Natural logarithm, dx, exact equation, ψy

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