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Mathematica |
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\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = 0
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
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\[
{}y^{\prime \prime }+25 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 1
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime } = 5
\] |
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\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5
\] |
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\[
{}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5
\] |
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\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\] |
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\[
{}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
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\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
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\[
{}y^{\prime \prime }+2 y = 2+{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8
\] |
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\[
{}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 \,{\mathrm e}^{2 x} x^{2}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime \prime \prime }-y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y = x^{2}
\] |
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\[
{}y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}}
\] |
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\[
{}y^{\prime \prime }-y = x \,{\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime } = x +\sin \left (\ln \left (x \right )\right )
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 3 x^{4}
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1
\] |
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\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x
\] |
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\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2
\] |
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\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x}
\] |
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\[
{}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\] |
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\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
\] |
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\[
{}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x}
\] |
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\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}}
\] |
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\[
{}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
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\[
{}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right )
\] |
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\[
{}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8
\] |
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\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
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\[
{}\left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\] |
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\[
{}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x
\] |
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\[
{}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x}
\] |
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\[
{}y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x}
\] |
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\[
{}2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0
\] |
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\[
{}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right ) = -{\mathrm e}^{t}, x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = t, 5 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = {\mathrm e}^{t}+2, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{-t}-1, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}+1]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = 1+{\mathrm e}^{t}, y^{\prime }\left (t \right )+2 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = {\mathrm e}^{t}+2, x^{\prime }\left (t \right )-x \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 3+{\mathrm e}^{t}]
\] |
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\[
{}\left (1-x \right ) y^{\prime } = x^{2}-y
\] |
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\[
{}x y^{\prime } = 1-x +2 y
\] |
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\[
{}x y^{\prime } = 1-x +2 y
\] |
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\[
{}y^{\prime } = 2 x^{2}+3 y
\] |
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\[
{}\left (1+x \right ) y^{\prime } = x^{2}-2 x +y
\] |
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\[
{}y^{\prime \prime }+x y = 0
\] |
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\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }+x^{2} y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0
\] |
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