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

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

\[ {}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \]

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = a^{2} y \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

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

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

\[ {}s^{\prime \prime }-a^{2} s = t +1 \]

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

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

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

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

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

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

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

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

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

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

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

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

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

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