# september 5

1. Solve separable ODEs:
1. $\sqrt{y^2+1}=xyy’;$
2. $y’=\cos(y-x)$
3. $y’-y=2x-3$
2. Solve
1. $(x-y)+(x+y)y’=0$
2. $2x^3y’=y(2x^2-y^2)$
3. $xy’-y=x\tan{y/x}.$
3. Sketch the slope fields and a few trajectories for
1. $y’=y^2-x;$
2. $y’=y-x^2;$
3. $y’=y^2+x^2-3.$

Where these trajectories have inflection points?

4. Sketch the slope field for
$\frac{dv}{dx}=-\frac{\sin(x)}{v}.$