- Solve linear ODE of 1st order:
- \[

y’+y\tan{x}=\sec{x};

\] - \[

xy+e^x=xy’;

\] - \[

(xy’-1)\ln{x}=2y.

\]

- \[
- Reduce the ODE to a linear one, and solve:
- \[

(x+1)(y’+y^2)=-y;

\] - \[

xy^2y’=^2+y^3;

\] - \[

xyy’=y^2+x.

\]

- \[
- Reduce order of the equation, and solve:
- \[

x^2y”=(y’)^2;

\] - \[

(y’)^2+2yy”=0;

\] - \[

y^3y”=1.

\]

- \[

# september 12

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