- Solve separable ODEs:
- \[

\sqrt{y^2+1}=xyy’;

\] - \[

y’=\cos(y-x)

\] - \[

y’-y=2x-3

\]

- \[
- Solve
- \[

(x-y)+(x+y)y’=0

\] - \[

2x^3y’=y(2x^2-y^2)

\] - \[

xy’-y=x\tan{y/x}.

\]

- \[
- Sketch the slope fields and a few trajectories for
- \[

y’=y^2-x;

\] - \[

y’=y-x^2;

\] - \[

y’=y^2+x^2-3.

\]

Where these trajectories have inflection points?

- \[
- Sketch the slope field for

\[

\frac{dv}{dx}=-\frac{\sin(x)}{v}.

\]

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