september 12

  1. Solve linear ODE of 1st order:
    1. \[
      y’+y\tan{x}=\sec{x};
      \]
    2. \[
      xy+e^x=xy’;
      \]
    3. \[
      (xy’-1)\ln{x}=2y.
      \]
  2. Reduce the ODE to a linear one, and solve:
    1. \[
      (x+1)(y’+y^2)=-y;
      \]
    2. \[
      xy^2y’=^2+y^3;
      \]
    3. \[
      xyy’=y^2+x.
      \]
  3. Reduce order of the equation, and solve:
    • \[
      x^2y”=(y’)^2;
      \]
    • \[
      (y’)^2+2yy”=0;
      \]
    • \[
      y^3y”=1.
      \]
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