> with(DEtools);

> ode3:=diff(y(x),x$2)+9*y(x)=0;

> dsolve(ode3,y(x));

> dsolve({ode3,y(0)=1,D(y)(0)=-2});

> phaseportrait(ode3,y(x),x=-1.5..1.5,[[y(0)=1,D(y)(0)=-2]],y=-2..2,arrows=none,thickness=2,title="Eks 3",linecolor=sin(x),stepsize=.02);

> ode4:=diff(y(x),x$2)+4*diff(y(x),x)+13*y(x)=0;

> dsolve(ode4,y(x));

> init4:=y(0)=5,D(y)(0)=1;

> dsolve({ode4,init4},y(x));

> phaseportrait(ode4,y(x),x=-0.5..2,[[init4]],y=-8..6,thickness=2,title="Eks 4",linecolor=[cos(2*x)],stepsize=.05);

> ode5:=diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=0;

> init5:=y(0)=10,D(y)(0)=-1;

> dsolve(ode5,y(x));

> dsolve({ode5,init5});

> phaseportrait(ode5,y(x),x=-1..2,[[init5]],y=-20..10,arrows=none,thickness=2,title="Eks 5",linecolor=sin(3*x),stepsize=.05);

> ode6:=diff(y(x),x$2)+diff(y(x),x)-2*y(x)=0;

> init6:=y(0)=1,D(y)(0)=2;

> dsolve(ode6,y(x));

> dsolve({ode6,init6},y(x));

> phaseportrait(ode6,y(x),x=-1.5..1.5,[[init6]],y=-6..6,arrows=none,thickness=2,title="Eks 6",linecolor=sin(x),stepsize=.05);

> ode8:=diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x^2;

> dsolve(ode8,y(x));

> ode9:=diff(y(x),x$2)+diff(y(x),x)-2*y(x)=exp(x);

> dsolve(ode9);

> phaseportrait(ode9,y(x),x=-2..2,[[y(0)=5,D(y)(0)=2]],y=0...80,title="Eks 9",arrows=none,linecolor=2*sin(x),stepsize=.05);

>