\[ {}w^{\prime } = w \cos \left (w\right ) \]

\[ \int _{0}^{w}\frac {1}{\textit {\_a} \cos \left (\textit {\_a} \right )}d \textit {\_a} +\int _{0}^{2}\frac {1}{w \cos \left (w \right )}d \textit {\_a} = t \] Verified OK.

\[ {}w^{\prime } = w \cos \left (w\right ) \]

\[ \int _{0}^{w}\frac {1}{\textit {\_a} \cos \left (\textit {\_a} \right )}d \textit {\_a} +\int _{0}^{-1}\frac {1}{w \cos \left (w \right )}d \textit {\_a} = t \] Verified OK.

\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \]

\[ \int _{}^{w}-\frac {1}{\left (-1+\textit {\_a} \right ) \sin \left (\textit {\_a} \right )}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \]

\[ \int _{}^{w}\frac {1}{3 \textit {\_a}^{3}-12 \textit {\_a}^{2}}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right ) \]

\[ \int _{}^{w}\frac {1}{\left (\textit {\_a}^{2}-2\right ) \arctan \left (\textit {\_a} \right )}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t +\frac {\sqrt {2}\, \operatorname {arccoth}\left (\frac {3 \sqrt {2}}{2}\right )}{2}-\frac {i \sqrt {2}\, \pi }{4} \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t +\frac {\sqrt {2}\, \operatorname {arccoth}\left (2 \sqrt {2}\right )}{2}-\frac {i \sqrt {2}\, \pi }{4} \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t +\frac {\sqrt {2}\, \operatorname {arccoth}\left (3 \sqrt {2}\right )}{2}-\frac {i \sqrt {2}\, \pi }{4} \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t -\frac {\sqrt {2}\, \operatorname {arccoth}\left (\sqrt {2}\right )}{2}+\frac {i \sqrt {2}\, \pi }{4} \] Verified OK.

\[ {}y^{\prime } = y^{2}-4 y+2 \]

\[ -\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\left (y-2\right ) \sqrt {2}}{2}\right )}{2} = t -3+\frac {\sqrt {2}\, \operatorname {arctanh}\left (\frac {\sqrt {2}}{2}\right )}{2} \] Verified OK.

\[ {}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \]

\[ \int _{}^{y}\frac {1}{\textit {\_a} \cos \left (\frac {\pi \textit {\_a}}{2}\right )}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

\[ \int _{}^{y}\frac {1}{\textit {\_a} \sin \left (\frac {\pi \textit {\_a}}{2}\right )}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = y^{3}-y^{2} \]

\[ \int _{}^{y}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

\[ \int _{}^{y}\frac {1}{\textit {\_a} \sin \left (\frac {\pi \textit {\_a}}{2}\right )}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = y^{2}-y^{3} \]

\[ \int _{}^{y}\frac {1}{-\textit {\_a}^{3}+\textit {\_a}^{2}}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3 \]

\[ \frac {y}{t^{2}+1}-3 \arctan \left (t \right ) = c_{1} \] Verified OK.

\[ {}y^{\prime } = \sin \left (t \right ) y+4 \]

\[ \int _{}^{t}-{\mathrm e}^{\cos \left (\textit {\_a} \right )} \left (\sin \left (\textit {\_a} \right ) y+4\right )d \textit {\_a} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right ) \]

\[ \int _{}^{t}\frac {\left (-y-4 \cos \left (\textit {\_a} \right ) \textit {\_a}^{2}\right ) {\mathrm e}^{\frac {1}{\textit {\_a}}}}{\textit {\_a}^{2}}d \textit {\_a} = c_{1} \] Verified OK.

\[ {}y^{\prime } = y+4 \cos \left (t^{2}\right ) \]

\[ \int _{}^{t}-{\mathrm e}^{-\textit {\_a}} \left (y+4 \cos \left (\textit {\_a}^{2}\right )\right )d \textit {\_a} = c_{1} \] Verified OK.

\[ {}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right ) \]

\[ \int _{}^{t}{\mathrm e}^{-\textit {\_a}^{2}+\frac {\sqrt {\pi }\, \operatorname {erf}\left (\textit {\_a} \right )}{2}} \left (-\cos \left (\textit {\_a} \right ) {\mathrm e}^{\textit {\_a}^{2}}+y\right )d \textit {\_a} +\left (-\left (\int _{}^{t}{\mathrm e}^{-\textit {\_a}^{2}+\frac {\sqrt {\pi }\, \operatorname {erf}\left (\textit {\_a} \right )}{2}}d \textit {\_a} \right )+{\mathrm e}^{\frac {\sqrt {\pi }\, \operatorname {erf}\left (t \right )}{2}}\right ) y = c_{1} \] Verified OK.

\[ {}y^{\prime } = -\sin \left (y\right )^{5} \]

\[ \int _{}^{y}-\frac {1}{\sin \left (\textit {\_a} \right )^{5}}d \textit {\_a} = t +c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \]

\[ -4 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (1+y\right )-\frac {t^{2}}{2}+3 \ln \left (t -1\right )+{\mathrm e}^{-y}-t = c_{1} \] Verified OK.

\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \]

\[ -\frac {t^{3}}{3}-t -\frac {1}{2 y^{2}} = -2 \] Verified OK.

\[ {}y^{\prime } = \frac {\left (1+t \right )^{2}}{\left (y+1\right )^{2}} \]

\[ -\frac {\left (t +1\right )^{3}}{3}+\frac {\left (y+1\right )^{3}}{3} = 0 \] Verified OK.

\[ {}y^{\prime } = \frac {t^{2}}{y+y t^{3}} \]

\[ -\frac {\ln \left (t^{3}+1\right )}{3}+\frac {y^{2}}{2} = 2 \] Verified OK.

\[ {}y^{\prime } = y^{2}-2 y+1 \]

\[ -\frac {1}{y-1} = t -1 \] Verified OK.

\[ {}y^{\prime } = 3-y^{2} \]

\[ \frac {\sqrt {3}\, \operatorname {arctanh}\left (\frac {y \sqrt {3}}{3}\right )}{3} = t \] Verified OK.

\[ {}y y^{\prime } = 2 x \]

\[ -\frac {x^{2}}{2}+\frac {y^{2}}{4} = c_{1} \] Verified OK.

\[ {}y^{\prime }-y^{3} = 8 \]

\[ \int _{}^{y}\frac {1}{\textit {\_a}^{3}+8}d \textit {\_a} = x +c_{1} \] Verified OK.

\[ {}\left (y-2\right ) y^{\prime } = x -3 \]

\[ \frac {y^{2}}{2}-\frac {x^{2}}{2}-2 y+3 x = c_{1} \] Verified OK.

\[ {}y^{\prime } = 3 x -y \sin \left (x \right ) \]

\[ \int _{}^{x}\left (-3 \textit {\_a} +y \sin \left (\textit {\_a} \right )\right ) {\mathrm e}^{-\cos \left (\textit {\_a} \right )}d \textit {\_a} = c_{1} \] Verified OK.

\[ {}y y^{\prime } = {\mathrm e}^{x -3 y^{2}} \]

\[ \frac {{\mathrm e}^{3 y^{2}}}{6}-{\mathrm e}^{x} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {x}{y} \]

\[ -\frac {x^{2}}{2}+\frac {y^{2}}{2} = c_{1} \] Verified OK.

\[ {}x y y^{\prime } = y^{2}+9 \]

\[ -\ln \left (x \right )+\frac {\ln \left (y^{2}+9\right )}{2} = c_{1} \] Verified OK.

\[ {}\cos \left (y\right ) y^{\prime } = \sin \left (x \right ) \]

\[ \cos \left (x \right )+\sin \left (y\right ) = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {x}{y} \]

\[ -\frac {x^{2}}{2}+\frac {y^{2}}{2} = 4 \] Verified OK.

\[ {}y y^{\prime } = x y^{2}+x \]

\[ -\frac {x^{2}}{2}+\frac {\ln \left (y^{2}+1\right )}{2} = \frac {\ln \left (5\right )}{2} \] Verified OK.

\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \]

\[ \frac {y^{2}+9-2 x \sqrt {x \left (y^{2}+9\right )}}{\sqrt {y^{2}+9}} = 3 \] Verified OK.

\[ {}y y^{\prime } = x y^{2}-9 x \]

\[ -\frac {x^{2}}{2}+\frac {\ln \left (y^{2}-9\right )}{2} = c_{1} \] Verified OK.

\[ {}y^{\prime } = {\mathrm e}^{x +y^{2}} \]

\[ \frac {\operatorname {erf}\left (y\right ) \sqrt {\pi }}{2}-{\mathrm e}^{x} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]

\[ -x^{3}-2 x +\frac {y^{3}}{2}-y^{2} = c_{1} \] Verified OK.

\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2} \]

\[ -\frac {x^{2}}{2}+\frac {y}{4}+\frac {1}{4 y} = c_{1} \] Verified OK.

\[ {}y^{\prime } = 3 x y^{3} \]

\[ -\frac {x^{2}}{2}-\frac {1}{6 y^{2}} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}} \]

\[ -2 x -\frac {2 x^{\frac {3}{2}}}{3}+\frac {2 y^{\frac {3}{2}}}{3}+2 y = c_{1} \] Verified OK.

\[ {}y^{\prime }-2 y = -10 \]

\[ \frac {\ln \left (y-5\right )}{2} = x +\frac {\ln \left (3\right )}{2} \] Verified OK.

\[ {}y y^{\prime } = \sin \left (x \right ) \]

\[ \frac {y^{2}}{2}+\cos \left (x \right ) = 9 \] Verified OK.

\[ {}y^{\prime } = \frac {y^{2}-1}{y x} \]

\[ -\ln \left (x \right )+\frac {\ln \left (y-1\right )}{2}+\frac {\ln \left (y+1\right )}{2} = \frac {\ln \left (3\right )}{2}+i \pi \] Verified OK.

\[ {}y^{\prime } x^{2}+3 x^{2} y = \sin \left (x \right ) \]

\[ \int _{}^{x}\frac {\left (3 \textit {\_a}^{2} y-\sin \left (\textit {\_a} \right )\right ) {\mathrm e}^{3 \textit {\_a}}}{\textit {\_a}^{2}}d \textit {\_a} = c_{1} \] Verified OK.

\[ {}y^{\prime }-3 y = 6 \]

\[ \frac {\ln \left (y+2\right )}{3} = x +\frac {\ln \left (7\right )}{3} \] Verified OK.

\[ {}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \]

\[ \frac {{\mathrm e}^{4 x} \left (9 x^{2}-12 x y+4 y^{2}+1\right )}{2} = c_{1} \] Verified OK.

\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \]

\[ -2 x -\frac {\sin \left (-4 y+8 x -3\right )}{4} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \]

\[ -\ln \left (x \right )+\frac {y^{2}}{2 x^{2}} = c_{1} \] Verified OK.

\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \]

\[ \frac {1+\sin \left (\frac {y}{x}\right )}{x} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {x -y}{x +y} \]

\[ -\frac {x^{2}}{2}+y x +\frac {y^{2}}{2} = {\frac {9}{2}} \] Verified OK.

\[ {}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{\frac {2}{3}} \]

\[ y^{\frac {1}{3}} = \left (-\cos \left (x \right )^{2}+c_{1} +\frac {1}{2}\right ) \csc \left (x \right ) \] Verified OK.

\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \]

\[ \frac {y^{2}+2 x}{2 x^{2}} = {\frac {11}{2}} \] Verified OK.

\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \]

\[ -\ln \left (x \right )+\frac {y^{3}}{3 x^{3}} = c_{1} \] Verified OK.

\[ {}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y} \]

\[ \sqrt {y} = \frac {x}{2}+\frac {c_{1}}{x^{\frac {1}{3}}} \] Verified OK.

\[ {}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )} \]

\[ -x +\cos \left (4 x -y\right ) = c_{1} \] Verified OK.

\[ {}\left (2 y x +2 x^{2}\right ) y^{\prime } = x^{2}+2 y x +2 y^{2} \]

\[ \frac {2 y}{x}+\frac {y^{2}}{x^{2}}-\ln \left (x \right ) = c_{1} \] Verified OK.

\[ {}y^{\prime }+\frac {y}{x} = x^{2} y^{3} \]

\[ \frac {-y^{2} x -\frac {1}{2 x^{2}}}{y^{2}} = c_{1} \] Verified OK.

\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

\[ -2 \,{\mathrm e}^{14 x}+\frac {y^{4} {\mathrm e}^{12 x}}{4} = c_{1} \] Verified OK.

\[ {}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right ) \]

\[ -x +\sin \left (y\right ) {\mathrm e}^{x} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {1}{y}-\frac {y}{2 x} \]

\[ y^{2} x -x^{2} = c_{1} \] Verified OK.

\[ {}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0 \]

\[ {\mathrm e}^{-x \left (-y^{2}+x \right )} = c_{1} \] Verified OK.

\[ {}2 y x +y^{2}+\left (2 y x +x^{2}\right ) y^{\prime } = 0 \]

\[ y \left (y+x \right ) x = c_{1} \] Verified OK.

\[ {}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

\[ \frac {\left (y^{3}+2 x^{2}\right )^{2}}{4}-\frac {y^{6}}{4} = c_{1} \] Verified OK.

\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \]

\[ -\frac {x^{2}}{2}+x +\frac {y^{3}}{2} = c_{1} \] Verified OK.

\[ {}1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0 \]

\[ y^{2} x^{3}+3 y^{2}+x = c_{1} \] Verified OK.

\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \]

\[ y x^{4}-\frac {y^{5}}{5} = c_{1} \] Verified OK.

\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \]

\[ -\ln \left (x \right )-\frac {\ln \left (y^{4}+1\right )}{4} = c_{1} \] Verified OK.

\[ {}y+\left (y^{4}-3 x \right ) y^{\prime } = 0 \]

\[ \frac {x}{y^{3}}+y = c_{1} \] Verified OK.

\[ {}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0 \]

\[ \cos \left (y\right ) x +\sin \left (y\right ) = c_{1} \] Verified OK.

\[ {}3 y+3 y^{2}+\left (2 x +4 y x \right ) y^{\prime } = 0 \]

\[ -\ln \left (x \right )-\frac {2 \ln \left (y \left (y+1\right )\right )}{3} = c_{1} \] Verified OK.

\[ {}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0 \]

\[ -\frac {y^{3}}{x^{2}}+y^{4} = c_{1} \] Verified OK.

\[ {}4 y x +\left (3 x^{2}+5 y\right ) y^{\prime } = 0 \]

\[ 2 x^{2} y^{\frac {3}{2}}+2 y^{\frac {5}{2}} = c_{1} \] Verified OK.

\[ {}6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \]

\[ 5 \left (y x \right )^{\frac {1}{5}} \left (x^{2} y^{2}+1\right )^{\frac {3}{5}} x = c_{1} \] Verified OK.

\[ {}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}} \]

\[ -\frac {\sqrt {y^{2}+x^{2}}}{x} = -\ln \left (x \right )+c_{1} \] Verified OK.

\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \]

\[ \frac {x^{2} y^{2}}{2}-6 x = c_{1} \] Verified OK.

\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \]

\[ \frac {x^{6}}{6}+\frac {y^{3} x^{3}}{3} = c_{1} \] Verified OK.

\[ {}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0 \]

\[ y^{2} x^{2}+y^{2}+x = c_{1} \] Verified OK.

\[ {}2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime } = 0 \]

\[ \frac {y}{x^{2}+1}+2 \arctan \left (x \right ) = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {1}{y x -3 x} \]

\[ \frac {y^{2}}{2}-\ln \left (x \right )-3 y = c_{1} \] Verified OK.

\[ {}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0 \]

\[ \sin \left (y\right ) x +\cos \left (y\right )+\sin \left (y\right ) y = c_{1} \] Verified OK.

\[ {}\sin \left (y\right )+\left (1+x \right ) \cos \left (y\right ) y^{\prime } = 0 \]

\[ -\ln \left (x +1\right )-\ln \left (\sin \left (y\right )\right ) = c_{1} \] Verified OK.

\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \]

\[ \frac {y^{2}}{2 x^{4}}+\frac {1}{x^{2}} = c_{1} \] Verified OK.

\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \]

\[ \frac {\ln \left (x^{2}+y^{2}\right )}{2}+2 \arctan \left (\frac {x}{y}\right ) = c_{1} \] Verified OK.

\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \]

\[ \frac {y^{4}}{4 x^{4}}-\frac {1}{2 x^{2}} = c_{1} \] Verified OK.

\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \]

\[ \frac {y^{3} {\mathrm e}^{-12 x}}{3}-2 \,{\mathrm e}^{-8 x} = c_{1} \] Verified OK.

\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \]

\[ \frac {x^{2} y^{2}}{2}+2 y^{5} = c_{1} \] Verified OK.

\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \]

\[ \frac {y^{2} {\mathrm e}^{-x^{2}}}{2}-{\mathrm e}^{3 x^{2}} = c_{1} \] Verified OK.

\[ {}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1 \]

\[ -\frac {x \left (x^{2}+\left (-3 y-9\right ) x +3 y^{2}+18 y+30\right )}{3}+\frac {\left (y+3\right )^{3}}{3} = c_{1} \] Verified OK.

\[ {}y^{\prime } = y^{3}-y^{3} \cos \left (x \right ) \]

\[ -\sin \left (x \right )+x +\frac {1}{2 y^{2}} = c_{1} \] Verified OK.

\[ {}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0 \]

\[ {\mathrm e}^{x y^{2}}-x^{2} = c_{1} \] Verified OK.

\[ {}x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime } = 0 \]

\[ -\frac {x^{2} \left (2 y-1\right )}{2}+\frac {y^{2}}{2} = c_{1} \] Verified OK.

\[ {}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right ) \]

\[ -{\mathrm e}^{-y}+\frac {c_{2} {\mathrm e}^{-2 x}}{2}-c_{3} = 0 \] Verified OK.

\[ {}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime } \]

\[ \frac {y^{3}}{3}-{\mathrm e}^{3 x}-\frac {5}{3} = 0 \] Verified OK.

\[ {}2 x -y-y y^{\prime } = 0 \]

\[ \frac {2 \ln \left (2 x +y\right )}{3}+\frac {\ln \left (y-x \right )}{3} = c_{1} \] Verified OK.

\[ {}y^{\prime } = -\frac {x}{y} \]

\[ -\frac {x^{2}}{2}-\frac {y^{2}}{2} = c_{1} \] Verified OK.