# 11.1  Explicit Solutions
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 11.1.
> restart; eq1:=diff(y(t), t) + 5*y(t) = 2*t;
> dsolve(eq1, y(t));

                          /d      \
                   eq1 := |-- y(t)| + 5 y(t) = 2 t
                          \dt     /


                 y(t) = 2/5 t - 2/25 + exp(-5 t) _C1

> dsolve({eq1, y(1)=2}, y(t));

                                        42 exp(-5 t)
                  y(t) = 2/5 t - 2/25 + -- ---------
                                        25  exp(-5)

> y:=evaln(y); eq2:=diff(y(t), t$2) + 6*diff(y(t), t) - 7*y(t) = 1;
> dsolve(eq2, y(t));

                                y := y


                    / 2      \
                    |d       |     /d      \
             eq2 := |--- y(t)| + 6 |-- y(t)| - 7 y(t) = 1
                    |  2     |     \dt     /
                    \dt      /


              y(t) = - 1/7 + _C1 exp(t) + _C2 exp(-7 t)

> dsolve({eq2, y(1)=3, D(y)(1)=2}, y(t));

                            exp(t)             7
           y(t) = - 1/7 + 3 ------ + 1/7 exp(1)  exp(-7 t)
                            exp(1)

>