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Mathematica |
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\[
{}y^{\prime }-y \tan \left (x \right ) = x
\] |
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\[
{}y^{\prime } = {\mathrm e}^{x -2 y}
\] |
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\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}}
\] |
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\[
{}x y^{\prime } = x +y
\] |
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\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime } = x +\frac {1}{x}
\] |
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\[
{}x y^{\prime }+2 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
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\[
{}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0
\] |
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\[
{}x y y^{\prime } = \left (1+x \right ) \left (1+y\right )
\] |
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\[
{}y^{\prime } = \frac {2 x -y}{y+2 x}
\] |
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\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
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\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
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\[
{}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
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\[
{}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 1
\] |
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\[
{}\left (y^{2}+x \right ) y^{\prime }+y-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }+8 y^{\prime }+15 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+25 y = 0
\] |
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\[
{}4 y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 1
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\] |
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\[
{}y^{\prime \prime }+y = x^{3}+x
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 y = x +{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 y = {\mathrm e}^{x}+2
\] |
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\[
{}y^{\prime \prime }-y = 2 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = x^{3}+\sin \left (x \right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2
\] |
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\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = A \cos \left (p x \right )
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-12 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
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\[
{}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = x^{2}+1
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8} = \frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x}+\sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}+{\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (2 x \right ) x
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \cos \left (2 x +3\right )
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+9 y = 8 \sin \left (x \right )
\] |
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\[
{}25 y^{\prime \prime }-30 y^{\prime }+9 y = 0
\] |
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\[
{}9 y^{\prime \prime }-6 y^{\prime }+y = \left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x}
\] |
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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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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+3 y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 4 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 4 y_{2} \left (x \right )-y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-y_{1} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-4 y_{2} \left (x \right )]
\] |
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\[
{}[2 y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), 2 y_{2}^{\prime }\left (x \right ) = 5 y_{2} \left (x \right )-3 y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = -2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 1, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )]
\] |
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\[
{}[2 y_{1}^{\prime }\left (x \right )+y_{2}^{\prime }\left (x \right )-4 y_{1} \left (x \right )-y_{2} \left (x \right ) = {\mathrm e}^{x}, y_{1}^{\prime }\left (x \right )+3 y_{1} \left (x \right )+y_{2} \left (x \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{2} \left (x \right )]
\] |
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\[
{}y^{\prime \prime }+\frac {y}{x^{2}} = 0
\] |
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\[
{}y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}} = 0
\] |
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\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )} = 0
\] |
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\[
{}y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x} = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x} = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x \left (1+x \right )}-\frac {y}{x \left (1+x \right )} = 0
\] |
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\[
{}y y^{\prime } = x
\] |
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\[
{}y^{\prime }-y = x^{3}
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = x
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )
\] |
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\[
{}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right )
\] |
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\[
{}y^{\prime }+y \ln \left (x \right ) = x^{-x}
\] |
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\[
{}x y^{\prime }+y = x
\] |
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\[
{}x y^{\prime }-y = x^{3}
\] |
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\[
{}x y^{\prime }+n y = x^{n}
\] |
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\[
{}x y^{\prime }-n y = x^{n}
\] |
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\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
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