Learning Enhancement Team
Worksheet:
Homogeneous First Order
Differential Equations
This worksheet has questions on homogeneous first order differential equations. Before
attempting the questions below, you could read the study guide: Homogeneous First Order
Differential Equations.
1. Which of these first order ordinary differential equations are homogeneous?
a.
xy
dx
dy
b.
x
dx
dy
y4
c.
0
22
x
y
y
d.
xy
yx
dx
dy
4
22
e.
xyyx 4
2
f.
02
2
xyyx
2. Show that the following first order ordinary differential equations are homogeneous:
a.
xy
dx
dy
x2
2
b.
2
24
x
xyy
dx
dy
c.
332 yxyyx
3. For the following first order ordinary differential equations, first check if they are
homogenous and then find their general solutions.
a.
y
dx
dy
x2
b.
xy
yx
dx
dy 22
2
c.
1
x
y
y
4. Find the particular solution to the following homogeneous first order ordinary
differential equations:
a.
04 22 yx
dx
dy
xy
where
71 y
b.
xy
dx
dy
x
where
21 y
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Homogeneous
First Order
Differential Equations
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