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1) The given family of functions is the general solution of the differential equation on the...

1) The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem.

y = c1 + c2 cos(x) + c3 sin(x), (−∞, ∞);

y''' + y' = 0,    y(π) = 0,    y'(π) = 8,    y''(π) = −1

y =

2) Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 10 grams of C is formed in 10 minutes. How much (in grams) is formed in 20 minutes? (Round your answer to one decimal place.)

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