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=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

Y is proportional to the difference of x and z

• y= x-z

• y= k(z-x)

• y= k(x-z)

• y= z-x

Tags

CCSS.6.EE.C.9

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

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

• $y=\ln\left|2x^2+c\right|$

• y = e^2x+c

• y = mx+b

dy/dx= x √y

Find the general solution

• √y = ln|4x| + c

• √y = (x)^-1 + c

• 2y^1/2 = ln|x| + c

• 1/2y^1/2 = ln|x| + c

y varies jointly with x and the square of z

• y= kxz²

• y= kx√z

• y= kxz

• kx²z

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

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

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

Let  $y=f\left(x\right)$  be the solution to the differential equation  $\frac{dy}{dx}=y-10x^2$ with the initial condition  $f\left(0\right)=3$  .  What is the approximation for  $f\left(0.4\right)$  
 if Euler’s method is used, starting at  $x=0$   with steps of size 0.2 ?

• 4.120

• 4.200

• 4.240

• 4.768

Let $y=g\left(x\right)$  be the solution to the differential equation  $\frac{dy}{dx}=xy-2$   with the initial condition  $g\left(2\right)=-1$ . What is the approximation for g(1)  if Euler’s method is used, starting at x=2  with two steps of equal size?

• -6.25

• 1.25

• 1.50

• 3.00

In drawing the slope field for the differential equation , I would place short slope lines of _________ at the points (0,1), (1,-1), and (2,-2)
  $\frac{dy}{dx}=2x-3y$  

Select all that apply

• -3

• -1

• 2

• 5

• 10

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSS.ID.C.7