DIFFERENTIAL EQUATIONS

Which of the following equations solves dy/dt = ky?

• y = y₀e^kt

• y = mx + b

• y = a(x - h)² + k

• y = Asin[B(x - C)] + D

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

• B

• C

• D

• E

Consider the differential equation
dy/dx = e^y(4x²-5x). Let y=f(x) be the particular solution to the differential equation that passes through (1, 0).
Write an equation of the line tangent to the graph of f at the point (1, 0).

• y=x-1
• y=2(x-1)
• y=-(x-1)
• y=-2(x-1)

Determine the order and degree.

• 1, 2
• 2, 2
• 1, 1
• 2, 1

Determine order and degree

• 3, 2
• 3, 5
• 5, 3
• 5, 2

Tags

CCSS.HSA.APR.A.1

Write a differential equation for the statement:

"The rate of change of P is proportional to the product of the present amount and 4 - P."

• dP/dt = kP

• dP/dt = k(4 - P)

• dP/dt = kP(4-P)

• dP/dt = kP/(4-P)

Find a solution for y if dy/dx = 2x√y and y = 4 when x = 3.

• 2√y = x² + C

• y = (x² + 25)²/4

• y = x⁴/4

• y = ¼(x² - 5)²

The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially?

• 1

• About 16

• About 40

• About 53

Tags

CCSS.HSF.LE.A.4

Find the particular solution for y if dy/dx = 2x√y and y = 4 when x = 3.

• 2√y = x² + C

• y = (x² + 25)²/4

• y = x⁴/4

• y = (x²/2-5/2)^1/2

Greenium has a half-life of 23 years and decays following the Law of Exponential Change. After how many years will 80% of an original amount have decayed?

• t = 7.4143 years

• t = 10.2646

• t = 53.4043 years

• t = 74.0341 years

Tags

CCSS.HSF.LE.A.4