Which of the following is a solution to the differential equation xy2y=2

?

y=x22

A

B

C

y=2x31

Answer C: y equals, 4 times x squared, minus 1

y=4x21

Answer B: y equals, x squared, plus 2 x

y=x2+2x

Answer A: y equals, x squared, minus 2

Let y=f(x)

be the solution to the differential equation dydx=3x+2y with the initial condition f(1)=0.5. What is the approximation for f(1.2) if Euler's method is used, starting at x=1

with two steps of size 0.1 ?

A

0.81

Answer A: 0.81

B

1.30

Answer B: 1.30

C

1.33

Answer C: 1.33

1.41

Let y=g(x)

be the solution to the differential equation dydx=1y with the initial condition g(1.5)=1. What is the approximation for g(0) if Euler's method is used, starting at x=1.5

with three steps of equal size?

5.75

A

B

C

0.75

Answer C: negative 3.50

3.50

Answer B: negative 4.00

4.00

Answer A: negative 5.75