Use the method of Examples $5,6,$ and $7$ to find general solutions of the systems in Problems $11$ through $20.$ If initial conditions are given, find the corresponding particular solution. For each problem, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given syste.

$11.x^{\text{'}}=y,y^{\text{'}}=-x$

$12.x^{\text{'}}=y,y^{\text{'}}=x$

$13.x^{\text{'}}=-2y,y^{\text{'}}=2x$;$x(0)=1,y(0)=0$

$14.x^{\text{'}}=10y,y^{\text{'}}=-10x$;$x(0)=3,y(0)=4$

$15.x^{\text{'}}=\frac{1}{2}y,y^{\text{'}}=-8x$

$16.x^{\text{'}}=8y,y^{\text{'}}=-2x$

$17.x^{\text{'}}=y,y^{\text{'}}=6x-y$;$x(0)=1,y(0)=2$

$18.x^{\text{'}}=-y,y^{\text{'}}=10x-7y$;$x(0)=2,y(0)=-7$

$19.x^{\text{'}}=-y,y^{\text{'}}=13x+4y$;$x(0)=0,y(0)=3$

$20.x^{\text{'}}=y,y^{\text{'}}=-9x+6y$