Differential Equations and Slope Fields

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

Find the Particular Solution

• $y=2+e^{\left(\frac{x^2}{2}+x\right)}$

• $y=2e^{\left(\frac{x^2}{2}+x\right)}$

• $y=\ln\left|\frac{x^2}{2}+x+1\right|+2$

• $y=\ln\left|\frac{x^2}{2}+x+e^2\right|$

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.1

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.4

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=Ce^5t

  B) P= 5e^418t

• A) P=Ce^5t

  B) P= 418e^5t

• A) P=Ce^t

  B) P= 418e^t

• A) P=Ce^10t

  B) P= 418e^10t

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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

• 
• 
• 
• 

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.CED.A.2

Water flows continuously from a large tank at a rate proportional to the amount of water in the tank, modeled by dy/dt = ky.  There was initially 10,000 ft^3 at t=0.  After 4 hours there were 8000 ft^3 remaining.
What is the value of k in the differential equation (calculator)

• -0.050
• -0.056
• -.169
• -.200

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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

Solve the Initial Value Problem

• $y=-\frac{1}{x}$

• $y=-x^2$

• $y=\frac{-1}{x+1}$

• $y=\frac{1}{x+1}$

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.D.10

The rate of change of the surface area of a cube, S, with respect to time,t, is directly proportional to the square root of one-sixth the surface area. Which of the following is a differential equation that best describes this relationship?

• $\frac{\text{d}S}{\text{d}t}=\frac{k}{\sqrt{6S}}$

• $\frac{dS}{dt}=k\sqrt{\frac{t}{6}}$

• $\frac{dS}{dt}=k\sqrt{\frac{S}{6}}$

• $S\left(t\right)=\frac{\sqrt{S}}{6}$

Tags

CCSS.HSA.SSE.A.1

Consider the differential equation dy/dx = x + 2y for which g(x) is the solution.  Which of the following statements is true if the particular solution contains (0,-1)

• g(x) is increasing and concave up
• g(x) is increasing and concave down
• g(x) is decreasing and concave up
• g(x) is decreasing and concave down

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the mistake if possible:

• The Diff EQ is solved correctly

• Step 1 is incorrect. The separation of variables wasn't done correctly.

• Step 2 is incorrect. They didn't integrate x² correctly.

• Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

Tags

CCSS.HSA.REI.A.1