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ODE |
Mathematica |
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\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2}
\] |
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\[
{}\left (2 x +5\right )^{2} y^{\prime \prime }-6 \left (2 x +5\right ) y^{\prime }+8 y = 0
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right )
\] |
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\[
{}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4
\] |
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\[
{}y^{\prime \prime \prime } x +\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x
\] |
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\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
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\[
{}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\] |
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\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y = 2
\] |
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\[
{}x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\] |
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\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
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\[
{}y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\] |
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\[
{}y^{\prime \prime } \cos \left (x \right )^{2} = 1
\] |
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\[
{}x^{3} y^{\prime \prime \prime } = 1
\] |
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\[
{}y^{\prime \prime \prime } \csc \left (x \right )^{2} = 1
\] |
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\[
{}y^{\prime \prime } \sqrt {a^{2}+x^{2}} = x
\] |
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\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
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\[
{}y^{3} y^{\prime \prime } = a
\] |
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\[
{}y^{\prime \prime }+\frac {a^{2}}{y} = 0
\] |
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\[
{}y^{\prime \prime } = y^{3}-y
\] |
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\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime \prime } = x y^{\prime }
\] |
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\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
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\[
{}y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = a x
\] |
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\[
{}x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime } x -x y^{\prime \prime }-y^{\prime } = 0
\] |
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\[
{}y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime } = x
\] |
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\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime } = a {y^{\prime }}^{2}
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}a^{2} y^{\prime \prime } y^{\prime } = x
\] |
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\[
{}y^{\prime \prime \prime } y^{\prime \prime } = 2
\] |
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\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
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\[
{}a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\] |
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\[
{}a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}y^{\prime } = x y^{\prime \prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime \prime } = \lambda y^{\prime \prime }
\] |
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\[
{}n \,x^{3} y^{\prime \prime \prime } = -x y^{\prime }+y
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2} = 3 y y^{\prime }
\] |
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\[
{}2 x^{2} y y^{\prime \prime }+y^{2} = x^{2} {y^{\prime }}^{2}
\] |
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\[
{}x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+y^{2} n}
\] |
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\[
{}x^{4} y^{\prime \prime } = \left (x^{3}+2 x y\right ) y^{\prime }-4 y^{2}
\] |
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\[
{}x^{4} y^{\prime \prime }-x^{3} y^{\prime } = x^{2} {y^{\prime }}^{2}-4 y^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime } = {\mathrm e}^{y}
\] |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+1 = 0
\] |
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\[
{}y^{\prime \prime } = \frac {1}{\sqrt {a y}}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
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\[
{}-a y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
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\[
{}\sin \left (y\right )^{3} y^{\prime \prime } = \cos \left (y\right )
\] |
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\[
{}{\mathrm e}^{x} \left (x y^{\prime \prime }-y^{\prime }\right ) = x^{3}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\] |
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\[
{}2 x y^{\prime \prime \prime } y^{\prime \prime } = {y^{\prime \prime }}^{2}-a^{2}
\] |
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\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
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\[
{}\left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y = 6
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\] |
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\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime } = y+{\mathrm e}^{x}
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }+\left (x +5\right ) y = {\mathrm e}^{x}
\] |
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\[
{}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+x y^{\prime }-y = X
\] |
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\[
{}y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = {\mathrm e}^{x} x^{3}
\] |
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\[
{}y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y = 0
\] |
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\[
{}\left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y
\] |
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\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = \sec \left (x \right ) {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
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