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1. Plot a direction field and typical solutions curve for the following differential equations:

a. dy/dx=sin(x)+sin(y)

b.dy/dx=sin(x-y)

c. dy/dx=x^2 -y

d. dy/dx=y-x+1

2. For each of the previous differential equations, determine, if possible, (just by looking at the plots) the following with the given initial conditions:

$\lim_{x\rightarrowin\infty }y(x)) . : \lim_{x\rightarrowin-\infty }x(y))$

justify your answer:

a. y(0)=0 and y(0)=-2

b. y(0)=0 and y(-5)=4

c. y(1)=0, y(1)=2, and y(-3)=3

d. y(0)=0, y(-3)=0 and y(1)=-2

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