An ice chest contains 9 cans of apple juice6 cans of grape juice5 cans of orange juiceand 4 cans of pineapple juice Suppose that
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Substitute , so that
, and
which is separable as
Integrate both sides with respect to . For the integral on the left, first split into partial fractions:
Solve for :
Replace and solve for
:
Now use the given initial condition to solve for :
so that the particular solution is