MAT136H1 Lecture : 9.3 Separable Equations Question #3 (Medium)

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8 Apr 2013

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Question #3 (medium): solution to differential equation that meet the initial condition. With the initial condition, the arbitrary constant factor which otherwise would be kept unknown can be determined, so to completely describe the solution of the differential equation. Find the solution to the differential equation that meet the initial condition. First the like variables need to be grouped together: have and removed: . Thus, setting them equal to each other again: Rearranging to have it written for y in terms of : ; cross multiplying to solve for c: ( ) ;

Related Questions

In Section, we looked at mixing problems in which the volume of fluid remained constant and saw that such problems give rise to separable differentiable equations. (See Example 6 in that section) If the rates of flow into and out of the system are different, then the volume is not constant and the resulting differential equation is linear but not separable.

A tank contains 100 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t) is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation