prelim1_2 - Prelim 1 Problem 3 dy 1 = t y t2 dx t y(1 = 1...

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Prelim 1: Problem 3 dy dx = 1 t - t y + t 2 y (1) = 1 Solution dy dx - 1 t - t y = t 2 dy dx + t - 1 t y = t 2 The integrating factor is ρ ( x ) = e ( t - 1 /t ) dx = e t 2 2 - ln t = e t 2 2 t Multiplying the given differential equation by the integrating factor, e t 2 2 t dy dx + t - 1 t y e t 2 2 t = t 2 e t 2 2 t d dx y e t 2 2 t = te t 2 2 y e t 2 2 t = te t 2 2 dx y e t 2
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