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.