Ordinary Diff Eq Exam Review Solutions 32

Ordinary Diff Eq Exam Review Solutions 32 - 34 1 Solutions...

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Unformatted text preview: 34 1 Solutions . Let or . Then and . An integrating factor is . Solving for gives Since . Integrating we get we get and solving for so we get . . Now . Substituting and simplifying gives . 19. Let . Then and so . Substituting and in standard form we get ,a we get separable diﬀerential equation. Clearly, is an equilibrium solution. Assume for now that . Then separating variables and simplifying using gives . Integrating we get to get equilibrium solution 20. Let . Now substitute and simplify , . (We absorb the constant in .) The becomes . . Then and so and in standard form we get . Substituting we get . We see that are equilibrium solutions. Separating variables we get fractions gives . Integrating and simplifying gives , However, the case substitute . Solving for , and simplify to get becomes . Then we get , . The . . In . Separating variables and simplifying . Integrating we get and simplify to get 22. Let . Then standard form we get . . Now and substituting we get standard form we get let we get gives the equilibrium solution equilibrium solution 21. Let . Partial . Now , and substituting we get . Notice that . , . In , are ...
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