Chapter 1.3, Problem 1E

To determine

(a)

To verify:

That the straight line $y=\pm 2x$ are solution curves for the direction field $dy/dx=4x/y$.

To determine

(b)

To sketch:

The solution curve with the initial condition $y\left(0\right)=2$ for $dy/dx=4x/y$.

To determine

(c)

To sketch:

The solution curve with the initial condition $y\left(2\right)=1$ for $dy/dx=4x/y$.

To determine

(d)

To find:

The behaviour of the above solution as $x\to +\infty$ and $x\to -\infty$.