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# 1_5b - Solutions 1.5-Page 51 Problem 27 Solve the...

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Solutions 1.5-Page 51 Problem 27 Solve the differential equation by regarding y as the independent variable rather than x. 1 ) ( = + dx dy ye x y The differential equation does not yet follow the general form given on pg.43. The derivative term ( dx dy ) is differentiating y with respect to x. Since y is the independent variable, it must be the other way around. Division by dx dy , and rearranging terms yields y ye x dy dx = dy e y = 1 ) ( ρ . This equation follows the form given on pg.43. The integrating factor is y e = Multiplying both sides by ) ( y gives y x e dy dx e y y = The left hand side is dy x e d y ) ( , so the equation becomes y dy x e d y = ) ( Integrating both sides gives C y x e ydy dy dy x e d y y + = = 2 ) ( 2 Dividing by gives y e + = C y e y x y 2 ) ( 2

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Problem 33 A tank contains 1000 liters (L) of a solution consisting of 100 kg of salt dissolved in water. Pure water is pumped into the tank at the rate of 5 L/s, and the mixture - kept
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1_5b - Solutions 1.5-Page 51 Problem 27 Solve the...

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