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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 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 youve 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 dierential equation satised by y . Solve this dierential equation to nd the amount of salt: (a) after t minutes (b) after 30 minutes (c) after a suciently long time 2...
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