′
(
0
)=8?
?
The initial conditions lead to the system of equations
which is equivalent to
The solution to the IVP is given by
.
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4. (8 points)
The following differential equation may be solved by either
performing a substitution to reduce it to a separable equation or by
performing a different substitution to reduce it to a homogeneous equation.
Display the substitution to use and perform the reduction,
but do not
attempt to solve the separable
or homogeneous equation you
obtain
.
The key to this puzzle is the solution to the linear system
which is equivalent to
,
geometrically, a pair of parallel lines.
Consequently, a suitable
substitution is given by
z
=
x
2
y
.
After a little routine algebra, the
reduction results in the separable DE
______________________________________________________________________
10 Point Bonus:
Although you will later learn a body of theory that will
make the solution of the following following 2rd order equation routine,
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 Fall '08
 STAFF
 Differential Equations, Derivative, Ode

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