\[ {}y^{\prime \prime }+\tan \relax (x ) y^{\prime }+y \cot \relax (x ) = 0 \]

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

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

\[ {}\sin \relax (x ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\cot \relax (x ) y^{\prime }-\csc \relax (x )^{2} y = \cos \relax (x ) \]

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

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

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

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

\[ {}\left (2 \sin \relax (x )-\cos \relax (x )\right ) y^{\prime \prime }+\left (7 \sin \relax (x )+4 \cos \relax (x )\right ) y^{\prime }+10 y \cos \relax (x ) = 0 \]

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

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

\[ {}y^{\prime \prime }+9 y = 0 \]

\[ {}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

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

\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

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

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

\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]

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

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

\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]

\[ {}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \]

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

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

\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]

\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \]

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]

\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]

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

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

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

\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]

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

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

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

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]

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

\[ {}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\relax (t )-\operatorname {Heaviside}\left (t -2\right )\right ) \]

\[ {}y^{\prime \prime }+9 y = 24 \sin \relax (t ) \left (\operatorname {Heaviside}\relax (t )+\operatorname {Heaviside}\left (-\pi +t \right )\right ) \]

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

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

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\relax (t )-\operatorname {Heaviside}\left (t -1\right )\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\relax (t )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]

\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\relax (t )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\relax (t )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\relax (t )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]

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

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \left (\delta \left (-\pi +t \right )\right )-5 \left (\delta \left (-2 \pi +t \right )\right ) \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]

\[ {}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

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

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

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \]

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