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\vbox{\halign{\bf#\hss\cr Math 226: Calculus IV\cr
Quiz 5\quad Feb.~23/25, 1993\cr
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1. Find an explicit function of x, y(x), which satisfies the initial value
problem
$$y' + y^2 = 1, \quad y(0) = 0$$

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2. A new home owner takes out a \$100,000 mortgage. The loan is to
be paid back evenly over 15 years at an annual interest rate  of
8\%. Let $p(t)$ denote the amount owed on the mortgage after $t$
years.  Assume the interest is compounded and mortgage payments
are made continuously. Determine the differential equation which
describes the function $p(t)$ using the constant $k$ to represent
what is paid back each year.  Solve the equation and use the fact
that $p(15) = 0$ to solve for $k$.

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