Homework #2 Math 527
The usual instructions: Solve the problems, simplifying the solution as much as you
can. AWE (Always Write Equations) and ADTSTTBSOTE (Always Do The Same Thing
To Both Sides Of The Equation). Your work should be clear, legible, organized, and
written on loose-leaf paper. Write your name, Math 527, section #, and HW2 in the
upper-right corner, and staple the pages together on the upper-left corner.
Problems 1-7: Determine if the ODE is an “exact equation.” If it is, find an implicit
solution, or an explicit solution if you can.
1. 2x + y − (x + 6y)
dy
dx = 0
2. 2x − 1 + (3y + 7)dy
dx = 0
3. 5t + 4y + (4t − 8y
3
)
dy
dt = 0
4. x2 − y
2 + (x
2 − 2xy)
dy
dx = 0
5. t
dy
dt = 2tet − y + 6t
2
6. (x + y)
2 + (2xy + x
2 − 1)dy
dx = 0
7. sin y − y sin x + (cos x + x cos y − y)
dy
dx = 0
