Math 3C Practice Test 1



Math 3C Practice Test 1

1. Consider the following differential equation:

[pic]

a) Sketch a slope field for this differential equation for values of t between -2 and 2, and values of y between -2 and 2.

b) What are the constant solutions to this differential equation, if any?

c) Classify any constant solutions as stable or unstable.

d) Sketch a solution to this differential equation with the initial condition y(0)=0.

e) Is this a separable differential equation? If so, find the general solution using separation of variables, and find the solution with the initial condition y(0)=0.

f) Is this a linear differential equation? If so, find the general solution by finding the homogeneous solution, then the particular solution, and adding the two.

2. Consider the following differential equation:

[pic]

a) Use Euler’s method to find y(1) with step sizes of 0.5 and 0.25.

b) Find the exact value for y(1) by solving the differential equation.

c) Is this a linear differential equation? Homogeneous? Constant coefficient?

3. Classify the following differential equations as linear, separable, both, or neither. If the differential equation is linear, further classify it as homogeneous or non-homogeneous, and constant coefficient or variable coefficient. If the differential equation is either linear or separable, then find the general solution.

a) [pic]

b) [pic]

c) [pic]

d) [pic]

4. Use the change of variable z = ln(y) to solve the non-linear differential equation:

[pic]

Where a and b are constants.

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