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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} 3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\]
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\[
{} \frac {x -2}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\]
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\[
{} y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\]
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\[
{} y^{\prime } = \sqrt {\frac {y}{t}}
\]
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\[
{} y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\]
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\[
{} y+y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\]
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\[
{} y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\]
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\[
{} \sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime } = 0
\]
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\[
{} t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0
\]
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\[
{} y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0
\]
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\[
{} 2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0
\]
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\[
{} 2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\]
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\[
{} 2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\]
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\[
{} 3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0
\]
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\[
{} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\]
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\[
{} 1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\]
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\[
{} 2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0
\]
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\[
{} \frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0
\]
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\[
{} {\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\]
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\[
{} 2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0
\]
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\[
{} y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0
\]
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\[
{} \cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\]
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\[
{} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\]
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\[
{} -2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0
\]
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\[
{} -4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0
\]
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\[
{} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0
\]
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\[
{} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\]
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\[
{} -1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0
\]
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\[
{} \cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0
\]
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\[
{} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y} = 0
\]
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\[
{} t^{2}+t y+y^{2}-t y y^{\prime } = 0
\]
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\[
{} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0
\]
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\[
{} t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0
\]
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\[
{} y^{\prime }+2 y = t^{2} \sqrt {y}
\]
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\[
{} -2 y+y^{\prime } = t^{2} \sqrt {y}
\]
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\[
{} t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0
\]
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\[
{} y^{\prime }+\cot \left (x \right ) y = y^{4}
\]
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\[
{} t y^{\prime }-{y^{\prime }}^{3} = y
\]
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\[
{} t y^{\prime }-y-2 \left (-y+t y^{\prime }\right )^{2} = y^{\prime }+1
\]
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\[
{} 1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\]
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\[
{} 1+2 y-2 t y^{\prime } = \frac {1}{{y^{\prime }}^{2}}
\]
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\[
{} y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5}
\]
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\[
{} y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3}
\]
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\[
{} y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1
\]
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\[
{} t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\]
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\[
{} t^{2}-y+\left (y-t \right ) y^{\prime } = 0
\]
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\[
{} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0
\]
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\[
{} y = t y^{\prime }+3 {y^{\prime }}^{4}
\]
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\[
{} y-t y^{\prime } = -2 {y^{\prime }}^{3}
\]
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\[
{} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0
\]
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\[
{} \sin \left (y\right )-\cos \left (t \right ) y+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0
\]
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\[
{} \frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = -x +y^{2}
\]
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\[
{} y^{\prime } = t y^{3}
\]
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\[
{} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\]
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\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\]
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\[
{} t y^{\prime \prime }+2 y^{\prime }+t y = -t
\]
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\[
{} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\]
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\[
{} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\]
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\[
{} \left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\]
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\[
{} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0
\]
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\[
{} 2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2}
\]
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\[
{} t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1
\]
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\[
{} \left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime } = -2-t
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\]
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\[
{} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right ) = 0
\]
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\[
{} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\]
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\[
{} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right ) = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+x y^{\prime } = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+\left (-1+y^{2}\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-\cos \left (x \right ) y = \sin \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+6 y = 0
\]
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\[
{} x \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-3 y = {\mathrm e}^{x} x
\]
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\[
{} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0
\]
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\[
{} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime } = 1
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}, y^{\prime }\left (t \right ) = {\mathrm e}^{t}]
\]
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\[
{} y^{\prime } = x^{2}+y^{2}
\]
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\[
{} y^{\prime } = \sqrt {x^{2}-y}-x
\]
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\[
{} y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\]
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\[
{} y^{\prime } = \sin \left (x y\right )
\]
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\[
{} y^{\prime } = -y^{2}+x^{2}
\]
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\[
{} y^{\prime } = -y^{2}+x^{2}
\]
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\[
{} y^{\prime } = x +y^{2}
\]
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