Separable Differential Equations Worksheets Page 2
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7Calculus Maximus
Notes 5.1: Separable Diff EQ
Example 2:
dy
2
Find the general and particular solutions to the separable differential equation
x y
given the initial
dx
and (b)
.
conditions (a)
f
0
1
f
0
2
Example 3:
AP 1998-4
such that for all points
Let f be a function with
f
(1) 4
, x y on the graph of f , the slope is given by
2
dy
3
x
1
.
dx
2
y
x .
(a) Find the slope of the graph of f at the point where
1
x and use it to approximate (1.2)
(b) Write an equation of the line tangent to the graph of f at
1
f
.
2
dy
3
x
1
(c) Find
f x by solving the separable differential equation
( )
with the initial
dx
2
y
.
condition (1) 4
f
(d) Use your solution from part (c) to find the exact value of
f
(1.2)
.
?
(e) What would the solution equation be if the initial condition were
f
(1)
4
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