45_pdfsam_math 54 differential equation solutions odd

45_pdfsam_math 54 differential equation solutions odd -...

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Exercises 2.3 Since driver B was 3 miles behind driver A at time t = 0, and his speed remained constant, he fnished the race at time t B =(3+2) /v B =5 /v B . At this moment, driver A had already gone s ( t B )= 1 ln 2 ln ( v B t B ln 2 + 1) = 1 ln 2 ln ± 5 v B v B ln 2 + 1 ² = 1 ln 2 ln (5 ln 2 + 1) 2 . 1589 > 2 miles , i.e., A won the race. EXERCISES 2.3: Linear Equations, page 54 1. Writing dy dx x 2 y = x 2 cos x, we see that this equation has the Form (4) on page 50 oF the text with P ( x )= x 2 and Q ( x )= x 2 cos x . ThereFore, it is linear. Isolating dy/dx yields dy dx = y cos x x 2 . Since the right-hand side cannot be represented as a product g ( x ) p ( y ), the equation is not
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Unformatted text preview: separable. 3. In this equation, the independent variable is t and the dependent variable is x . Dividing by x , we obtain dx dt = sin t x t 2 . ThereFore, it is neither linear, because oF the sin t/x term, nor separable, because the right-hand side is not a product oF Functions oF single variables x and t . 5. This is a linear equation with independent variable t and dependent variable y . This is also a separable equation because dy dt = y ( t 1) t 2 + 1 = t 1 t 2 + 1 y = g ( t ) p ( y ) . 41...
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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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