Chapter 14.1, Problem 25PS

a.

To determine

The particular solution of the differential equation $\frac{dy}{dx}=x+y$ containing the point $\left(1,2\right)$ .

b.

To determine

The sketch of the solution of the differential equation $\frac{dy}{dx}=x+y$ through $\left(1,2\right)$ using direction field and compare the result with part-(a).

c.

To determine

The solution of the differential equation $\frac{dy}{dx}=x+y$ for $x_0=1,y_0=1\text{ and }h=0.2$ .