Download MATH 2243 Summer 2012 Worksheet 1

MATH 2243
Worksheet 1
Summer 2012
Topics: the notion of a differential equation; separable differential equations.
1. Verify that the function y = Cx3 , where C is some constant, is a solution of the differential
equation 3y − xy 0 = 0.
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2. Determine if the function y = 3 − e−x is a solution of the equation xy 0 + 2y = e−x .
3. For which values of a the function y = cos ax becomes a solution of the equation y 00 +10y =
0?
4. Solve a separable differential equation.
a) y 0 = 3y
b) xy 0 − y = 0
c)
dy
dx
=
1+y
1−x
d) z 0 = 10x+z
e) xy 0 + y = y 2
Hint: Recall the product rule (uv)0 = u0 v + uv 0 .
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