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