Chapter 7 Differential Equations

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

• A) P=P₀e^5t

  B) P= 5e^418t

• A) P=P₀e^5t

  B) P= 418e^5t

• A) P=P₀e^t

  B) P= 418e^t

• A) P=P₀e^10t

  B) P= 418e^10t

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

• P=.05e^1000t

• P=1000e^5t

• P=1000e^.05t

• p=lne^1000t

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

dy/dx = 2x/e^2y find the general solution

• y = ln (2x²/2 + C) / 2

• y = ln(2x²/2)+c

• y = e^2x+c

• y = mx+b

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

• 𝑦 = ln(15t)

• 𝑦 = 16t³

• 𝑦 = (2𝑡³ − 16)^1/2

• 𝑦 = (2𝑡³ −16)

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.5

Dy/dx= tanx+15x2+e^x+1/x

• y= -ln|sinx| + 5x³ + e^x + ln|x| + c

• y= secxtanx + 5x³ + e^x + ln|x| + c

• y= -ln|cosx| + 5x³ + e^x + ln|x| + c

• y= sec²(x) + 5x³ + e^x + ln|x| + c

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

The particular solution is

• B

• C

• D

• E

Tags

CCSS.HSA.REI.A.1

Which choice below represents this slope field?

• dy/dx = 2x

• dy/dx = -x

• dy/dx = x

• dy/dx = x²

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which equation below represents the slope field?

• dy/dx = x - 2

• dy/dx = 1/2x + 1

• dy/dx =1/2 y - 2

• dy/dx = y + 2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Which functions below will have the same slope field? (choose all that apply)

• y = x² - 3

• y = x² + 4

• y = 2x - 5

• y = 2x²

Tags

CCSS.HSS.ID.C.7

Which slope field is represented by dy/dx = x²?

• 
• 
• 
• 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10