\[ {}t \cot \left (x\right ) x^{\prime } = -2 \]

\[ {}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

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

\[ {}x^{\prime } = 2 x+\operatorname {Heaviside}\left (-1+t \right ) \]

\[ {}x^{\prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]

\[ {}x^{\prime } = x-2 \operatorname {Heaviside}\left (-1+t \right ) \]

\[ {}x^{\prime } = -x+\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \]

\[ {}x^{\prime }+3 x = \delta \left (-1+t \right )+\operatorname {Heaviside}\left (t -4\right ) \]

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

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

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

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

\[ {}y^{\prime }+4 x y = 8 x \]

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

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

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

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

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

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

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

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

\[ {}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0 \]

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

\[ {}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

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

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

\[ {}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]

\[ {}\frac {2 y^{\frac {3}{2}}+1}{x^{\frac {1}{3}}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0 \]

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

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

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

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

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

\[ {}\frac {1+8 x y^{\frac {2}{3}}}{x^{\frac {2}{3}} y^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) y^{\prime }}{y^{\frac {4}{3}}} = 0 \]

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

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

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

\[ {}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \]

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

\[ {}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \]

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

\[ {}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0 \]

\[ {}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0 \]

\[ {}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0 \]

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

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

\[ {}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0 \]

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

\[ {}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0 \]

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

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

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

\[ {}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0 \]

\[ {}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \]

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

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

\[ {}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0 \]

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

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

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

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

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

\[ {}x^{4} y^{\prime }+2 x^{3} y = 1 \]

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

\[ {}y^{\prime }+4 x y = 8 x \]

\[ {}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}} \]

\[ {}\left (u^{2}+1\right ) v^{\prime }+4 u v = 3 u \]

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

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

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

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

\[ {}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right ) \]

\[ {}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0 \]

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

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

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

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

\[ {}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0 \]

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

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

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

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

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

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

\[ {}x^{\prime }-x = \sin \left (2 t \right ) \]

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

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

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \]

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \]

\[ {}\left (2+x \right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \]

\[ {}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \]

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

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

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

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

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

\[ {}y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \]

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

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