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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \]

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

\[ {}y^{\prime \prime }+16 y = 4 \delta \left (-3 \pi +t \right ) \]

\[ {}y^{\prime \prime }+y = \delta \left (-\pi +t \right )-\delta \left (-2 \pi +t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]

\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (-\pi +t \right ) \cos \left (t \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (-\pi +t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1 \]

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

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

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

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

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

\[ {}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \]

\[ {}2 x \sqrt {1-y^{2}}+y^{\prime } y = 0 \]

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

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

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

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

\[ {}z^{\prime } = 10^{x +z} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \]

\[ {}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

\[ {}y^{\prime } = \frac {x +3 y-5}{x -y-1} \]

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \]

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

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

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

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

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

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

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

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

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

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