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Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
MATH 308 Homework 3
3.1. Determine whether the equation
(3x2 − 2xy + 2) dx + (6y 2 − x2 + 3) dy = 0
is exact. If it is exact, find the general solution.
3.2. Find the value of b for which the equation
(xy 2 + bx2 y) dx + (x + y)x2 dy = 0
is exact, and then solve it using that value of b.
3.3. Find the general solution of the differential equation
6y 00 − y 0 − y = 0.
3.4. Find the solution of the initial value problem
y 00 − y = 0,
5
y(0) = ,
4
3.5. Find the Wronskian of the pair of function
e2t ,
e−3t/2 .
3
y 0 (0) = − .
4
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