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

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

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

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

\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \]

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

\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \]

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

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

\[ {}x^{\prime \prime }+x = 3 \left (\delta \left (-2 \pi +t \right )\right ) \]

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

\[ {}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (-10+t \right ) \]

\[ {}[x^{\prime }\relax (t ) = -3 y \relax (t ), y^{\prime }\relax (t ) = 2 x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -2 y \relax (t ), y^{\prime }\relax (t ) = -4 x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t ), y^{\prime }\relax (t ) = 2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 4 y \relax (t ), y^{\prime }\relax (t ) = 2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 2 x \relax (t )-y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -2 x \relax (t )-3 y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )+4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -3 y \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -2 x \relax (t ), y^{\prime }\relax (t ) = x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -2 x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = -4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -6 y \relax (t ), y^{\prime }\relax (t ) = 6 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+3 y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )-14] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+3 y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )-1] \]

\[ {}[x^{\prime }\relax (t ) = -x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = -3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )-4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = -3 x \relax (t )+3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )-4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = -3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -3 x \relax (t )+4 y \relax (t ), y^{\prime }\relax (t ) = -3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+2 y \relax (t ), y^{\prime }\relax (t ) = 6 x \relax (t )+3 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = -5 x \relax (t )+3 y \relax (t ), y^{\prime }\relax (t ) = 2 x \relax (t )-10 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t ), y^{\prime }\relax (t ) = 2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )-y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )-4 y \relax (t ), y^{\prime }\relax (t ) = x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 9 y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )+4 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-y \relax (t )+1, y^{\prime }\relax (t ) = x \relax (t )+y \relax (t )+2] \]

\[ {}[x^{\prime }\relax (t ) = -5 x \relax (t )+3 y \relax (t )+{\mathrm e}^{-t}, y^{\prime }\relax (t ) = 2 x \relax (t )-10 y \relax (t )] \]

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

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )+2 y \relax (t )+3, y^{\prime }\relax (t ) = 7 x \relax (t )+5 y \relax (t )+2 t] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-3 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+7 y \relax (t )] \]

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

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

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

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

\[ {}{y^{\prime }}^{2}-4 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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