For the differential equation
\[ y' = \frac{x}{y} \]
(a) Plot a direction field in the rectangle R[\( (-4 \lt x \lt 4 ) \) \( (-4 \lt y \lt 4 ) \)].
(b) Sketch some solution curves on the direction field.
Solve
For the differential equation
\[ y' = x - y \]
(a) Plot a direction field in the rectangle R[\( (-4 \lt x \lt 4 ) \) \( (-4 \lt y \lt 4 ) \)].
(b) Sketch some solution curves on the direction field.
Solve
A direction field is shown above.
Which of the four differential equations below could generate this direction field?
\[ \begin{align}
\frac{dy}{dx} &= x^2 - y^2 \quad &(A)\\
\frac{dy}{dx} &= \frac{y+xy}{x} \quad &(B)\\
\frac{dy}{dx} &= -\frac{x}{y} \quad &(C)\\
\frac{dy}{dx} &= 2y \quad &(D)\\
\end{align}\]
Solve