# solutions1bd - Math 33b Quiz 1bd Name UCLA ID 1 Using any...

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Math 33b, Quiz 1bd, January 17, 2008 Name: UCLA ID: 1. Using any technique possible, find the solution to the initial-value problem dy dx + 4 x x 2 + 1 y = 1 , y (0) = - 2 . Solution. The differential equation is linear, so we want to multiply both sides by the integrating factor e R 4 x x 2 +1 dx = e 2 log( x 2 +1) = ( x 2 + 1) 2 : ( x 2 + 1) 2 dy dx + 4 x ( x 2 + 1)
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Unformatted text preview: y = ( x 2 + 1) 2 d dx [ y ( x 2 + 1) 2 ] = x 4 + 2 x 2 + 1 y ( x 2 + 1) 2 = x 5 5 + 2 x 3 3 + x + C y = 1 ( x 2 + 1) 2 ( x 5 5 + 2 x 3 3 + x + C ) Using the initial condition y (0) =-2, we have-2 = C , so y ( x ) = 1 ( x 2 + 1) 2 ( x 5 5 + 2 x 3 3 + x-2) . 1...
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• Spring '07
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• Math, UCLA ID, -2. dx

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