1. Choose the differential equation corresponding to this direction field
Choose the differential equation corresponding to this direction field. {image}
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Choose the equation which solution is graphed and satisfies the initial condition y ( 0 ) = 8. {applet}
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. The solution of the differential equation {image} satisfies the initial condition y ( 0 ) = 6. Find the limit {image}
0.6 -2
doesn't exist 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Use Euler's method with step size 0
Use Euler's method with step size 0.2 to estimate y( 1 ), where y( x ) is the solution of the initial-value problem. Round your answer to four decimal places. y ' = x + y 2, y( 0 ) = 0
y ( 1 ) =
y ( 1 ) =
y ( 1 ) =
y ( 1 ) = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Program a calculator to use Euler's method with step size h = 0
Program a calculator to use Euler's method with step size h = 0.4 to compute the approximate value of y(0.4) where y(x) is the solution of the initial-value problem {image}
0.4 2 9 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50