Answer: Classify each differential equation as separable, exact, linear, homogeneous, or

Chapter 2, Problem 8

(choose chapter or problem)

Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.

(a) \(\frac{d y}{d x}=\frac{x-y}{x}\)

(b) \(\frac{d y}{d x}=\frac{1}{y-x}\)

(c) \((x+1) \frac{d y}{d x}=-y+10\)

(d) \(\frac{d y}{d x}=\frac{1}{x(x-y)}\)

(e) \(\frac{d y}{d x}=\frac{y^{2}+y}{x^{2}+x}\)

(f) \(\frac{d y}{d x}=5 y+y^{2}\)

(g) \(y d x=\left(y-x y^{2}\right) d y\)

(h) \(x \frac{d y}{d x}=y e^{x y}-x\)

(i) \(x y y^{\prime}+y^{2}=2 x\)

(j) \(2 x y y^{\prime}+y^{2}=2 x^{2}\)

(k) \(y d x+x d y=0\)

(l) \(\left(x^{2}+\frac{2 y}{x}\right) d x=\left(3-\ln x^{2}\right) d y\)

(m) \(\frac{d y}{d x}=\frac{x}{y}+\frac{y}{x}+1\)

(n) \(\frac{y}{x^{2}} \frac{d y}{d x}+e^{2 x^{3}+y^{2}}=0\)