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1.  Which of the following seperable differential equations do you get if you begin with the homogeneous equation \(\frac{dy}{dx} = \frac{x^2 + 3y^2}{2xy}\) and use the variable substitution \(v = y/x\)?

b.  \(v + x \frac{dv}{dx} = \frac{1 + 3v^2}{2v}\).

b.  \(v + x \frac{dv}{dx} = \frac{v^2 + 3}{2v}\).

c.  \(v + x \frac{dv}{dx} = \frac{2v}{v^2 + 3}\).

d.  \(v + x \frac{dv}{dx} = \frac{2v}{1 + 3v^2}\).

e.  \(v + x \frac{dv}{dx} = \frac{v + 3}{2v^2}\)

Please hand in questions 2, 3, and 4 (but remember to click submit for question 1).

2.  Finish solving the differential equation from question 1.

3. Solve the following differential equation: \(y' + y^2 \sin x = 0\)

4.  Solve the following initial value problem: \(y' - y = 2te^{2t}\), \(y(0) = 1\)