\[ {}x^{\prime }+5 x = t \]

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

\[ {}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]

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

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

\[ {}\theta ^{\prime \prime }+4 \theta = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

\[ {}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

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

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

\[ {}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

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

\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

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

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

\[ {}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

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

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

\[ {}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

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

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

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

\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0 \]

\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+20 y \left (t \right ), y^{\prime }\left (t \right ) = 40 x \left (t \right )-19 y \left (t \right )] \]