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ODE |
Mathematica |
Maple |
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\[
{}\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime \prime } = x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime } = x^{2} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime } = \sec \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
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\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
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\[
{}y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\] |
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\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime } = 0
\] |
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\[
{}x^{4} y^{\prime \prime } = \left (-x y^{\prime }+y\right )^{3}
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime } = x^{2} y^{\prime }-y^{2}
\] |
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\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
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\[
{}\sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
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\[
{}\left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x}
\] |
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\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0
\] |
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\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\] |
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\[
{}\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\] |
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\[
{}x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2}
\] |
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\[
{}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0
\] |
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\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = {\mathrm e}^{x} x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\] |
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\[
{}y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-y \cot \left (x \right ) = \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x}
\] |
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\[
{}[x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
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\[
{}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
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\[
{}[t x^{\prime }\left (t \right ) = t -2 x \left (t \right ), t y^{\prime }\left (t \right ) = t x \left (t \right )+t y \left (t \right )+2 x \left (t \right )-t]
\] |
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