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52_pdfsam_math 54 differential equation solutions odd

# 52_pdfsam_math 54 differential equation solutions odd - P x...

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Chapter 2 Table 2–B : Successive approximations for y (3) using Simpson’s rule. Number of Intervals y ( 3 ) 6 0.183905 8 0.183291 10 0.183110 12 0.183043 Since the last 3 approximate values do not change by more than 5 in the fourth place, it appears that their Frst three places are accurate and the approximate solution is y (3) 0 . 183 . 27. (a) The given di±erential equation is in standard form. Thus P ( x )= 1+sin 2 x .S i n c e we cannot express R P ( x ) dx as an elementary function, we use fundamental theorem of calculus to conclude that, with any Fxed constant a , x Z a P ( t ) dt 0 = P (
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Unformatted text preview: P ( x ). Since, in the formula for µ ( x ), one can choose any antiderivative of P ( x ), we take the above deFnite integral with a = 0. (Such a choice of a comes from the initial point x = 0 and makes it easy to satisfy the initial condition.) Therefore, the integrating factor µ ( x ) can be chosen as µ ( x ) = exp x Z p 1 + sin 2 t dt . Multiplying the di±erential equaion by µ ( x ) and integrating from x = 0 to x = s , we obtain d [ µ ( x ) y ] dx = µ ( x ) x ⇒ d [ µ ( x ) y ] = µ ( x ) x dx 48...
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