1. 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

2. Choose the equation which solution is graphed below and that satisfies the initial condition y ( 0 ) = 1. {applet}
{image} 1. 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

3. Use Euler's method with step size 0
Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3, and y4 of the solution of the initial-value problem y ' = 1 + 7x - 4y, y( 1 ) = 2
y 1 = 0, y 2 = 7.75, y 3 = -4.25, y 4 = 21.5
y 1 = -0.5, y 2 = 8.25, y 3 = -5.75, y 4 = 24
y 1 = 1.5, y 2 = 4.25, y 3 = 2.25, y 4 = 8
y 1 = 2, y 2 = 3.75, y 3 = 3.75, y 4 = 5.5 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

4. Use Euler's method with step size 0. 25 to estimate y( 0
Use Euler's method with step size 0.25 to estimate y( 0.5 ), where y( x ) is the solution of the initial-value problem. Round your answer to two decimal places. y ' = 4xy 2, y( 0 ) = 1
y(0.5) =2.03
y(0.5) =1.20
y(0.5) =1.06
y(0.5) =1.25 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. Kirchhoff's Law gives us the derivative equation {image} If Q(0) = 0, use Euler's method with step size 0.3 to estimate Q after 0.9 second.
3.6
3.024
2.88 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