1. (3pts) Verify that MATH is a solution of the differential equationMATH

  2. (5pts ea.) Solve the following differential equations

    1. MATH

    2. MATH

    3. MATH

    4. MATH

    5. MATH

  3. (8pts) A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing $\frac{1}{2}$ pounds of salt per gallon is pumped into the tank at a rate of 6 gallons per minute.. The well mixed solution is then pumped out at a slower rate of 4 gallons per minute.. Find the number of pounds of salt in the tank after 3 minutes. If the capacity of the tank is 400 gallons, find the number of pounds of salt in the tank just as it overflows.

  4. (4pts) Given that MATH is a two parameter family of solutions of MATH on the interval MATH can you find a solution of the differential equation satisfying the initial conditions MATH Is the solution unique? Do your answers contradict the existence and uniqueness theorem? Explain.

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