Differential Equations Review

Which of the following represents a possible slope field for the differential equation: $\frac{dy}{dx}=x^2$  

• 
• 
• 
• 

Of the following, which is a solution to the differential equation? 

Select all that apply:
 $y''-y=0$  

•  $y=\sin\left(x\right)$  

•  $y=e^x$  

Given the differential equation  $\frac{dP}{dt}=5P$  

A) Find the general solution to this DE. 
B) Find the particular solution to this DE given the condition 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

Check all that apply:  $e^{kt+C_1}=$  

•  $e^{kt}\cdot e^{C_1}$  

•  $e^{kt}\cdot C$  

•  $Ce^{kt}$  

•  $e^{kt\cdot C}$  

Which of the following differential equations can be shown with this slope field?

• dy/dx = -x

• dy/dx = x²

• dy/dx = x/y

• dy/dx = y/x

I want to solve the differential equation $\frac{dy}{dx}=6-y$  . 

Which of the following represents this function when variables are separated?

•  $\frac{dy}{dx}+y=6$  

•  $dy+y=6dx$  

•  $\frac{dy}{6-y}=dx$  

•  $dy=\left(6-y\right)dx$  

The rate of change of M is proportional to M. Which differential equation models this verbal statement?

• $\frac{dy}{dt}=kt$

• $y=Ce^{kt}$

• $\frac{dM}{dt}=kM$

• $M=Ce^{kt}$

Radium (²²⁶Ra) has a half life of 1599 years. Given an initial amount of 6 grams of Radium, how many grams will remain after one half-life?

• 3 grams

• 6 grams

• 12 grams

• 36 grams

Tags

CCSS.HSF.LE.A.4