A brief Differential equation homework.

MAP 2302 - Fall 2017 Test 1 - Take Home Part Date Name

You must show all work for credit.

You may use your notes and book.

You must do all work on your own without any help.

Due Tuesday October 3rd at the BEGINNING of class.

1. Find the orthogonal trajectories of the family of curves y = ln (tan x + c1).

Solve the following differential equations. You may use any appropriate method. Show how you determine or state that they are Homogeneous, Exact, Linear, or Bernoulli’s if you use those methods. Do not solve for y explicitly EXCEPT where stated.

2. dx

dy − 1 =

x

y +

y2

x2

3. −x2 dy

dx + xy = x2y2 sin x

4. Solve the initial value problem dx

dy (y + sin x) y =

( 1

2 + y2 + cos x− 2xy

) y(0) =

√ 2

5. Verify that y = 4e2x cos(3x) is a solution to the differential equation

d2y

dx2 − 4

dy

dx + 13y = 0