midterm 1, september 29

  1. Solve
    \[
    y’=\cos^2(2y-x).
    \]
  2. Sketch the slope field
    \[
    y’=y-x^2.
    \]
    Find where the solutions to this differential equation have horizontal inflection points.
  3. \[
    x^3yy’=x^4+x^2y^2+y^4;
    \]
  4. Reduce to a linear DE and solve:
    \[
    y’=y^4\cos(x)+y\tan(x).
    \]
  5. Solve
    \[
    yy”-2(y’)^2=0.
    \]
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