Differential Equations and Slopefields

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

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

• y = ln (2x/2 + C)

  2

• y = ln(2x/2)+c

• y = e^2x+c

• y = mx+b

Which choice below represents this slope field?

• dy/dx = 2x

• dy/dx = -x

• dy/dx = yx

• dy/dx = x²

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

• 
• 
• 
• 

dy/dx = 4x/y.  Suppose y(0)=1
The particular solution is

• B
• C
• D
• E

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

Find the Particular Solution

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

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

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

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

Find the integral:

• 1/3(x⁴ + 3)³ + c

• 1/12(x⁴ + 3)³ + c

• 3/4(x⁴ + 3)³ + c

• 1/4(x⁴ + 3)³ + c

Find the integral:

• 1/8(4x² + 3)⁴ + c

• 1/2(4x² + 3)⁴ + c

• 1/32(4x² + 3)⁴ + c

• 1/4(4x² + 3)⁴ + c

 $\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$ 

•  $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$ 

•  $5x^{\frac{1}{3}}-4e^{-4x}+1+C$ 

•  $\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$ 

• Got lazy with fake answers