\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \]

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

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \]

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \]

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \]

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

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

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime } = 6 \,{\mathrm e}^{x} \sin \left (x \right ) x \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \]

\[ {}y^{\prime \prime }+9 y = 39 \,{\mathrm e}^{2 x} x \]

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \]

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

\[ {}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \]

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \]

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

\[ {}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right ) \]

\[ {}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \]

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \]

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \]

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \]

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

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

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right ) \]

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]

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

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

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

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

\[ {}y^{\prime \prime }-36 y = 0 \]

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

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

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

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

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

\[ {}y^{\prime \prime }-8 y^{\prime }+25 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \]

\[ {}y^{\prime \prime }+y^{\prime }-30 y = 0 \]

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