lecture3.mws

> with(plots):with(DEtools):

Warning, the name changecoords has been redefined

> de:=16*diff(y(t),t$2)-8*diff(y(t),t)+145*y(t)=0;

de := 16*diff(y(t), `$`(t, 2))-8*diff(y(t), t)+145*y(t) = 0

> sol:=dsolve({de,y(0)=-2,D(y)(0)=1});

sol := y(t) = 1/2*exp(1/4*t)*sin(3*t)-2*exp(1/4*t)*cos(3*t)

> sol:=solve(sol,y(t));

sol := 1/2*exp(1/4*t)*sin(3*t)-2*exp(1/4*t)*cos(3*t)

> plot(sol,t=0..10);

[Plot]

>

> de:=diff(y(t),t$2)-diff(y(t),t)+1/4*y(t)=0;

de := diff(y(t), `$`(t, 2))-diff(y(t), t)+1/4*y(t) = 0

> sol:=dsolve({de,y(0)=2,D(y)(0)=1/3});

sol := y(t) = 2*exp(1/2*t)-2/3*exp(1/2*t)*t

> sol:=solve(sol,y(t));

sol := 2*exp(1/2*t)-2/3*exp(1/2*t)*t

> plot(sol,t=0..3.5);

[Plot]

> sol2:=solve(dsolve({de,y(0)=2,D(y)(0)=2}),y(t));

sol2 := 2*exp(1/2*t)+exp(1/2*t)*t

> plot({sol,sol2},t=0..3,y=0..6);

[Plot]

> sol3:=solve(dsolve({de,y(0)=2,D(y)(0)=0.65}),y(t)):

> plot({sol,sol2,sol3},t=0..3,y=0..6);

[Plot]