DiffEQ Practice 1

The following Differential Equation is
 $\frac{\text{d}y}{\text{d}x}=\frac{e^y}{e^x}$  

• Separable.

• Non Separable.

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.

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

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

• B

• C

• D

• E

Tags

CCSS.HSA.REI.A.1

Find the general solution of the differential equation y’–ysin(x)=0.

• $|y|=Ce^{-\sin\left(x\right)}$

• $|y|=Ce^{\sin\left(x\right)}$

• $|y|=Ce^{-\cos\left(x\right)}$

• $|y|=Ce^{\cos\left(x\right)}$

• $|y|=-Ce^{\cos\left(x\right)}$

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

• $y=2e^{\frac{-9+x^3}{3}}$

• $y=-2e^{\frac{-9+x^3}{3}}$

• $y=\sqrt{\frac{2x^3}{3}}$

• $y=\sqrt{\frac{2x^3}{3}-14}$

• $y=-\sqrt{\frac{2x^3}{3}-14}$

Which of the following differential equations match the graph above?

 

•  $\frac{\text{d}y}{\text{d}x}=y^2-1$  

•  $\frac{\text{d}y}{\text{d}x}=x^2-1$  

•  $\frac{\text{d}y}{\text{d}x}=y^2+1$  

•  $\frac{\text{d}y}{\text{d}x}=x^2+1$  

Suppose y=f(x) is a particular solution to the differential equation dy/dx=x–y such that f(0)=0. Use the slope field above to estimate the value of f(2).

• -2

• -1

• 0

• 1

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

• 
• 
• 
• 

Shown above is a slope field for which of the following differential equations?

• $\frac{dy}{dx}=1+x$

• $\frac{dy}{dx}=x^2$

• $\frac{dy}{dx}=x+y$

• $\frac{dy}{dx}=\frac{x}{y}$