Worksheet 5.1 - Separable Differential Equations With Answers - Calculus Maximus Page 3
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3Calculus Maximus
WS 5.1: Separable Diff EQ
Free Response
For problems 9 – 18, find the general solution to the following differential equations, then find the
particular solution using the initial condition. You may have to factor and/or rewrite the expression in
order to separate your x-factors and y-factors.
dy
x
dy
x
dy
y
9.
,
y
1
2
10.
,
y
4
3
11.
,
y
2
2
dx
y
dx
y
dx
x
dy
dy
dy
2
y
0
3
= xy + 5x + 2 y +10 ,
y
0
1
y
0
0
12.
2
xy
,
13.
14.
cos
y
,
dx
dx
dx
4
y
ln
x
dy
dy
2
15.
2
xy
,
y
1
0.25
16.
,
y e
1
dx
dx
x
dy
dy
x y
y
sin
x
y
0
2
y
0
0
*17.
e
,
*18.
sec
x
e
,
dx
dx
*Xtra Spicy (requires manipulation prior to separation like Example 4 from Notes)
Page 3 of 4
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