Unformatted text preview: (c) In the interval x > 2, we have P ( x ) = 3. Therefore, the integrating factor is given by µ ( x ) = exp ±Z 3 dx ² = e 3 x . Multiplying the equation by this factor and solving yields e 3 x dy dx + 3 e 3 x y = xe 3 x ⇒ D x ( e 3 x y ) = xe 3 x ⇒ e 3 x y = Z xe 3 x dx . Integrating by parts and dividing by e 3 x gives y = e − 3 x ³ 1 3 xe 3 x − 1 9 e 3 x + C ´ = x 3 − 1 9 + Ce − 3 x . 52...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, ex dy, equation dy, ex yields

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