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ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime } x -2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y = \left (x -2\right ) {\mathrm e}^{2 x}
\] |
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✓ |
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\[
{}y^{\prime \prime } x -y^{\prime }+4 x^{3} y = x^{5}
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y = {\mathrm e}^{2 x}
\] |
✓ |
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\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }+2 x y = 2 x
\] |
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\[
{}\left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\] |
✓ |
✓ |
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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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\[
{}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 2 x^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\] |
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\[
{}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\] |
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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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\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
✓ |
✓ |
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\[
{}\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\] |
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\[
{}2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2}
\] |
✓ |
✓ |
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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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\[
{}\left (x +2\right ) y^{\prime \prime }-\left (2 x +5\right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\] |
✓ |
✓ |
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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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\[
{}y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\] |
✗ |
✗ |
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\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
✓ |
✓ |
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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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\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime } x -y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime } \cos \left (x \right )+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\] |
✓ |
✓ |
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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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\[
{}y^{\prime \prime } x +\left (x -1\right ) y^{\prime }-y = x^{2}
\] |
✓ |
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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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