The differential equation is and the point is
.
Slope field is .
Now draw a solution curve so that it move parallel to the near by segments.
\(a)
\Graph:
\Graph of differential equation and two approximate solutions:
\The differential equation is .
Integrate on each side.
\Basic integral formula : .
Solution function of the differential equation is .
Substitute in above solution to find the
value.
Substitute in solution function.
.
Graph:
\Graph the solution function .
(a)
\Graph of the differential equation and two approximate solutions is
\(b)
\Graph of the solutions is
.