Problems 2-6: 1, 2, 3, 5, 6, 9

Also: Solve the following differential equations:

1. $x\frac{dy}{dx} + y = x^4y^3$
2. $\frac{dy}{dx} + y = -y^3$, $y(0) = 1$
3. $\frac{dy}{dx} - y = -6e^xy^{\frac{3}{2}}$, $y(0) = \frac{1}{4}$

Answers:

1. $y^2 = \frac{1}{cx^2 - x^4}$
2. $y = \frac{1}{\sqrt{2e^{2x} - 1}}$
3. $y = \frac{1}{4}e^{-2x}$