Fill in the blank and then write this result as a linear first-order differential equation that is free of the symbol c₁ and has the form dy/dx = f(x, y). The symbols c₁ and k represent constants.

Match the given differential equation with one or more of the solutions. (Select all that apply.)

(a) Give the domain of the function

y = x^3/4.

(b) Give the largest interval I of definition over which

y = x^3/4

is a solution of the differential equation

4xy' − 3y = 0.

What is the slope of the tangent line to the graph of the solution of

y' = 7

y

 + 4x³

that passes through

(−1, 16)?

1

Fill in the blanks.

Construct an autonomous first-order differential equation

dy/dx = f(y)

whose phase portrait is consistent with the given figure.

dy dx

=

1

Use Euler's method with step size h = 0.1 to approximate y(1.2) where y(x) is a solution of the initial-value problem

y' = 3 + x

y

, y(1) = 9.

(Round your answer to two decimal places.)
1

Air containing 0.06% carbon dioxide is pumped into a room whose volume is 8000 ft³. The air is pumped in at a rate of 2000 ft³/min, and the circulated air is then pumped out at the same rate. If there is an initial concentration of 0.2% carbon dioxide, determine the subsequent amount in the room at any time.

A(t)

=

1

What is the concentration at 10 minutes? (Round your answer to three decimal places.)
2%

What is the steady-state, or equilibrium, concentration of carbon dioxide?
3%

Answer without referring back to the text. Answer true/false.

Answer without referring back to the text. Fill in the blank.