power series method

power series method - about 2 4 about 1 2 1 about 4 3 about...

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Faculty of Engineering and Technology Chemical Engineering Department Mathematical Methods for Chemical Engineers H.W. 3 Q1 . Using the power series method show that the following differential equation 1 + + = y x dx dy has a solution of the form ( ) ( ) 2 2 0 + = x e a x y x about x = 0 , where a 0 is a constant. Q2 . Solve the initial value problem () () 0 0 , 1 0 , 0 2 2 = = = + y y y e dx y d x () 0 0 y , 2 = = y x dx dy () () 3 1 y , 2 1 y , 0 2 2 = = = + dx dy dx y d x Q3 . Using power series method, find at least the fourth approximation for the following differential equation y e dx dy x + = Q4 . Solve the following differential equations
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Unformatted text preview: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) about , 2 4 about , 1 2 1 about , 4 3 about , 2 1 2 1 1 about , 1 1 2 about , 1 10 8 2 2 3 2 2 = = + + ′ + ′ ′ = = − + ′ − + ′ ′ = = + ′ + ′ ′ = = + + ′ + − ′ ′ + = = − ′ + + ′ ′ − = = − + ′ + ′ ′ x y x y x y x x y x y x y x x y x y y x x y x y x x y x x x y y x y x x x y x y x y x...
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This note was uploaded on 02/21/2011 for the course CE 0905231 taught by Professor Yousefmubarak during the Spring '11 term at University of Jordan.

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