Unformatted text preview: Âµ ( x ) = exp Â³Z Â´ âˆ’ 1 x Âµ dx Â¶ = e âˆ’ ln x = 1 x , for x > . Multiplying the equation by this integrating factor yields 1 x dy dx âˆ’ y x 2 = e x â‡’ D x Â· y x Â¸ = e x . Integrating gives y x = e x + C â‡’ y = xe x + Cx. Now applying the initial condition, y (1) = e âˆ’ 1, we have e âˆ’ 1 = e + C â‡’ C = âˆ’ 1 . 44...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Natural logarithm, dx

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