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Unformatted text preview: y , that is x ( y ), and use the identities: dy dx = 1 dx dy , d 2 y dx 2 =d 2 x d 2 y 1 ± dx dy ² 3 or, more concisely y = 1 x , y 00 =x 00 ( x ) 3 to rewrite the DE. Hint 2: Try a substitution u = x (once you’ve manipulated the DE). 3. A tank initially contains 5 kg of salt dissolved in 100 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at the same rate. If y ( t ) is the amount of salt in the tank (in kg) after t minutes, write down the diﬀerential equation satisﬁed by y . Solve this diﬀerential equation to ﬁnd the amount of salt: (a) after t minutes (b) after 30 minutes (c) after a suﬃciently long time 2...
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 Fall '07
 Anoymous
 Math, Calculus, Trigraph, Constant of integration, Complex number

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