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Differential Equations Quiz #3 March 11, 2005
Name____________________ R. Hammack Score ______
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(1) Find the orthogonal trajectory of +3
y=c.
Differentiating implicitly with respect to x gives
3y'+6x y+3
y'=0,
from which we get y'=-
Thus, the orthogonal trajectory must have D.E.
=
or 2x y dy =(
+
)dx
This is a homogeneous differential equation.
We use the substitution y = ux, dy = x du +u dx.