55_pdfsam_math 54 differential equation solutions odd

55_pdfsam_math 54 differential equation solutions odd - = 1...

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Exercises 2.3 Table 2–D : Euler’s method approximations for the solution of y 0 + y 1+sin 2 x = x , y (0) = 2, at x =1w ith h =0 . 1. k x k y k k x k y k k x k y k 0 0.0 2.0000 4 0.4 1.3584 8 0.8 1.0304 1 0.1 1.8000 5 0.5 1.2526 9 0.9 0.9836 2 0.2 1.6291 6 0.6 1.1637 10 1.0 0.9486 3 0.3 1.4830 7 0.7 1.0900 Table 2–E : Euler’s method approximations for the solution of y 0 + y 1+sin 2 x = x , y (0) = 2, at x =1w ith h =0 . 05. n x n y n n x n y n n x n y n 0 0.00 2.0000 7 0.35 1.4368 14 0.70 1.1144 1 0.05 1.9000 8 0.40 1.3784 15 0.75 1.0831 2 0.10 1.8074 9 0.45 1.3244 16 0.80 1.0551 3 0.15 1.7216 10 0.50 1.2747 17 0.85 1.0301 4 0.20 1.6420 11 0.55 1.2290 18 0.90 1.0082 5 0.25 1.5683 12 0.60 1.1872 19 0.95 0.9892 6 0.30 1.5000 13 0.65 1.1490 20 1.00 0.9729 29. In the presented form, the equation
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Unformatted text preview: = 1 e 4 y + 2 x is, clearly, not linear. But, if we switch the roles of variables and consider y as the independent variable and x as the dependent variable (using the connection between derivatives of inverse functions, that is, the formula y ( x ) = 1 /x ( y )), then the equation transforms to dx dy = e 4 y + 2 x dx dy 2 x = e 4 y . This is a linear equation with P ( y ) = 2. Thus the integrating factor is ( y ) = exp Z ( 2) dy = e 2 y 51...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.

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