Solve the given nonlinear plane autonomous system by changing to polar coordinates.

$x^{\text{'}}=y+x(x^2+y^2)$

$y^{\text{'}}=-x+y(x^2+y^2),x(0)=(4,0)$

$(r(t),(t))=($solution of initial value problem$)$

Describe the geometric behavior of the solution that satisfies the given initial condition.

The solution satisfies $r0$ as $t\frac{1}{32}$ and is a spiral.

The solution satisfies $r$ as $t\frac{1}{32}$ and is a spiral.

The solution satisfies $r0$ as $t$ and is a spiral.

The solution satisfies $r0$ as $t\frac{1}{32}$ and is not a spiral.

The solution satisfies $r$ as $t\frac{1}{32}$ and is not a spiral.