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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\]
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\[
{} y^{\prime } = x^{2} \left (1+y^{2}\right )
\]
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\[
{} y^{\prime } = \frac {x^{2}}{1-y^{2}}
\]
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\[
{} y^{\prime } = \frac {3 x^{2}+4 x +2}{2 y-2}
\]
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\[
{} x y^{\prime }-2 \sqrt {x y} = y
\]
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\[
{} y^{\prime } = \frac {x +y-1}{x -y+3}
\]
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\[
{} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\]
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\[
{} y^{2}-x y+x^{2} y^{\prime } = 0
\]
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\[
{} x +y-\left (x -y\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y}
\]
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\[
{} y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t}
\]
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\[
{} y^{\prime } = -\frac {y}{t}-1-y^{2}
\]
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\[
{} y y^{\prime }+x = a {y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{2}-a^{2} y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2} = 4 x^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 0
\]
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\[
{} s^{\prime \prime }+2 s^{\prime }+s = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 3 x +1
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{2 x} x
\]
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\[
{} y^{\prime \prime }+y = 4 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0
\]
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\[
{} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right )
\]
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\[
{} \sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0
\]
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\[
{} 3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0
\]
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\[
{} x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2}
\]
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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right )
\]
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\[
{} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0
\]
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\[
{} x x^{\prime \prime }-{x^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \left (x \right )
\]
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\[
{} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = x^{3}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\]
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\[
{} y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{2} = a^{2}-y^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0
\]
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\[
{} y \left (1+x^{2} y^{2}\right )+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0
\]
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\[
{} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}} = 0
\]
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\[
{} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0
\]
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\[
{} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0
\]
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\[
{} \left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1
\]
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\[
{} a y^{\prime \prime } y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}}
\]
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\[
{} a^{2} y^{\prime \prime \prime \prime } = y^{\prime \prime }
\]
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\[
{} y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\]
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\[
{} x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\]
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\[
{} \left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0
\]
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\[
{} \left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (1+x \right ) \eta ^{\prime }+\left (k +1\right ) \eta = 0
\]
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\[
{} x^{2}+y^{2}-2 x y y^{\prime } = 0
\]
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\[
{} x^{2}-y^{2}+2 x y y^{\prime } = 0
\]
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\[
{} x y^{\prime }-y = x^{2}+y^{2}
\]
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\[
{} x y^{\prime }-y = x \sqrt {x^{2}-y^{2}}\, y^{\prime }
\]
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\[
{} x +y y^{\prime }+y-x y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 16 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-8, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3]
\]
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\[
{} y^{\prime } = {\mathrm e}^{3 x}+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = x +2
\]
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\[
{} y^{\prime \prime \prime } = x^{2}
\]
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\[
{} y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} y^{\prime }+\cos \left (x \right ) y = \sin \left (x \right ) \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+k^{2} y = 0
\]
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\[
{} y^{\prime }+5 y = 2
\]
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\[
{} y^{\prime \prime } = 3 x +1
\]
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\[
{} y^{\prime } = k y
\]
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\[
{} y^{\prime }-2 y = 1
\]
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\[
{} y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime }-2 y = x^{2}+x
\]
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\[
{} 3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime }+3 y = {\mathrm e}^{i x}
\]
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\[
{} y^{\prime }+i y = x
\]
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\[
{} L y^{\prime }+R y = E
\]
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\[
{} L y^{\prime }+R y = E \sin \left (\omega x \right )
\]
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\[
{} L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x}
\]
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\[
{} y^{\prime }+a y = b \left (x \right )
\]
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