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Unformatted text preview: xvplane for the system in (a) is dv dx = − x + 1 / ( λ − x ) v . This equation is separable. Separating variables and integrating, we obtain v dv = ± − x + 1 λ − x ² dx ⇒ Z v dv = Z ± − x + 1 λ − x ² dx ⇒ 1 2 v 2 = − 1 2 x 2 − ln  λ − x  + C 1 ⇒ v 2 = C − x 2 − 2 ln  λ − x  ⇒ v = ± p C − x 2 − 2 ln( λ − x ) . (The absolute value sign is not necessary because x < λ .) 304...
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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.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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