Chapter 10.1, Problem 9E

To determine

(a)

Whether the equation $xy\text{'}-9y^2=0$ is separable or not and write it in the form $y\text{'}=f(x)g(y)$.

To determine

(b)

Whether the equation $\sqrt{4-x^2}y\text{'}=e^{3y}\sin x$ is separable or not and write it in the form $y\text{'}=f(x)g(y)$.

To determine

(c)

Whether the equation $y\text{'}=x^2+y^2$ is separable or not and write it in the form $y\text{'}=f(x)g(y)$.

To determine

(d)

Whether the equation $y\text{'}=9-y^2$ is separable or not and write it in the form $y\text{'}=f(x)g(y)$.