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Stewart_Calc_7ET ch09sec03
MULTIPLE CHOICE
1. Solve the differential equation.
a.
b.
c.
d.
e.
2. Solve the differential equation.
a.
b.
c.
d.
e.
3. A curve passes through the point and has the property that the slope of the curve at
every point P is times the y-coordinate P. What is the equation of the curve?
a.
b.
c.
d.
e.
4. Find the orthogonal trajectories of the family of curves.
a.
b.
c.
d.
e.
5. Solve the differential equation.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Solve the differential equation.
2. Experiments show that if the chemical reaction
takes place at , the rate of reaction of dinitrogen pentoxide is proportional to its
concentration as follows :
How long will the reaction take to reduce the concentration of to 50% of its original
value?
3. Solve the differential equation.
4. A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at
a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the
same rate. How much salt is in the tank after minutes?
5. Find the orthogonal trajectories of the family of curves.
6. is the family of solutions of the differential equation , find the
solution that satisfies the initial condition .
7. Find the solution of the differential equation that satisfies the initial condition
.
8. Solve the differential equation.
9. A certain small country has $20 billion in paper currency in circulation, and each day $70
million comes into the country's banks. The government decides to introduce new currency
by having the banks replace old bills with new ones whenever old currency comes into the
banks. Let denote the amount of new currency in circulation at time t with .
Formulate and solve a mathematical model in the form of an initial-value problem that
represents the ”flow” of the new currency into circulation (in billions per day).
10. Find the solution of the differential equation that satisfies the initial condition .
