Differential Equations Review

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?

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

• B
• C
• D
• E

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.

Find f(1) given f'(x)

• -12

• 0

• 14

• 20

Find the Particular Solution

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

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

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

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

Of the following, which is a solution to the differential equation, select all that apply:
 $y''-6y'+8y=0$  

•  $y=2\sin\left(4x\right)$  

•  $y=3e^{2x}$  

•  $y=Ce^{4x},\$  where C is a constant

Match the following differential equation with the correct slope field: dy/dx=x–y^2.

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Which of the following is the solution to the differential equation dy/dx=(x^2)/y with initial condition y(3)=-2?

• $y=2e^{\frac{-9+x^3}{3}}$

• $y=-2e^{\frac{-9+x^3}{3}}$

• $y=\sqrt{\frac{2x^3}{3}}$

• $y=\sqrt{\frac{2x^3}{3}-14}$

• $y=-\sqrt{\frac{2x^3}{3}-14}$

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