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