lecture4.mws

> s1:=(A*t^2+B*t+C)*exp(3*t);

s1 := (A*t^2+B*t+C)*exp(3*t)

> ls:=diff(s1,t$2)+9*s1;

ls := 2*A*exp(3*t)+6*(2*A*t+B)*exp(3*t)+18*(A*t^2+B*t+C)*exp(3*t)

> rs:=t^2*exp(3*t);

rs := t^2*exp(3*t)

> ls-rs;

2*A*exp(3*t)+6*(2*A*t+B)*exp(3*t)+18*(A*t^2+B*t+C)*exp(3*t)-t^2*exp(3*t)

> d:=simplify((ls-rs)/exp(3*t));

d := 2*A+12*A*t+6*B+18*A*t^2+18*B*t+18*C-t^2

> d:=collect(d,t);

d := (18*A-1)*t^2+(18*B+12*A)*t+2*A+18*C+6*B

> A:=1/18;

A := 1/18

> d;

1/9+(18*B+2/3)*t+18*C+6*B

> B:=-2/(3*18);

B := (-1)/27

> d;

-1/9+18*C

> C:=1/(9*18);

C := 1/162

> d;

0

> s1;

(1/18*t^2-1/27*t+1/162)*exp(3*t)

>

> simplify(diff(s1,t$2)+9*s1);

t^2*exp(3*t)

> s2:=D;

s2 := D

> ls:=diff(s2,t$2)+9*s2;

ls := 9*D

>