1)

with(plots):
implicitplot3d( x+5=((z-3)^2)/4+(y^2)/7,x=-10..10,y=-12..12, z=-12..12);


2)

plot( [ 20*sin(Pi*t/20), 20*(1-cos(Pi*t/20)),t=0..2*Pi] );

3)

plot([1+8*sin(3*t),t,t=0..2*Pi],coords=polar);


4)
with(inttrans):
invlaplace((p+3)/(p^3+2*p^2+3*p), p, t);

Ну а 5 самостоятельно.