Chapter 1.1, Problem 47P

(a)

Program Plan Intro

To find: The value of $C$ so that $y\left(10\right)=10$ .

(b)

Program Plan Intro

To find: The value of constant C or not and also find by inspection that a solution of $\frac{dy}{dx}=y^2$ such that $y\left(0\right)=0$ .

(c)

Program Plan Intro

To verify: That any given point $\left(a,b\right)$ in the plane, the differential equation $\frac{dy}{dx}=y^2$ has exactly one solution $y\left(x\right)$ satisfying the condition $y\left(a\right)=b$ .