The differential equation is
.
Rewrite the equation as
.
(a)
\Graph the slope field
.
(b)
\The differential equation is
.
The equation is in the form of
.
The differential equation is a first order linear differential equation.
\Solution of the first order linear differential equation is
is
.
Here
and
.
Find
.


.
.
The solution of differential equation is
.
Substitute
and
.


.
The solution of the differential equation is
.
The solution of the differential equation is passing through the points
and
.
Substitute
in
.



.
Substitute
in
.
.
The particular solution passing through the point
is
.
Substitute
in
.



.
Substitute
in
.
.
The particular solution passing through the point
is
.
(c)
\Graph the particular solutions
and
on the slope field.
(a)
\Graph of the slope field
.
(b)
\The particular solution passing through the point
is
.
The particular solution passing through the point
is
.
(c)
\Graph the particular solutions
and
on the slope field.