Math 305

Homework Set 2

Due Friday, August 29

I. Solve the following separable differential equations. Find the general solution if no initial condition is present.

1. y' = y and y(0)=-6

2. y' = y and y(1) = e2

3. y' = cos(2x) + 2 and y(pi) = 8

4. y' = y2ex and y(0)=2

5. y' = ex+y

II. Describe the set of initial conditions for which each differential equation equation below is guaranteed to satisfy Theorem 2.4.2. Do not try to solve them.

1. y' = (x+2y)/(2-y)

2. y' = x3/(x+2y)

3. y' = y/(x-3) + x2/(y+4)

4. y' = tan(x)/(y2-1)

5. y' = cot(xy)

6. y' = sqrt(y)/(x+y3)

7. y' = (xy)2/3 + ln(xy)

III. Draw the direction field by hand for the following differential equations. Do not solve these equations.

1. y' = 2x-1

2. y' = (x/2) + 2

3. y' = y+1

4. y' = 2x+y

5. y' = (1/3)(x2-1)

6. y' = y ex

7. y' = 3x-y

8. y' = y-x

9. y' = x2-4

10. y' = (3y+1)/x