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ODE |
Mathematica |
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\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1
\]
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\[
{} 4 y^{\prime \prime }+y = x^{4}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x
\]
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\[
{} y^{\prime \prime }+y = x^{4}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 2
\]
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\[
{} y^{\prime \prime }+y^{\prime } = 3 x^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 a y^{\prime }+y a^{2} = 0
\]
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\[
{} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+x^{2} y = 0
\]
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\[
{} y^{\prime \prime }+y a^{2} = f \left (x \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = t
\]
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\[
{} y^{\prime \prime }-y^{\prime } = t^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\]
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\[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\]
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\[
{} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0
\]
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\[
{} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0
\]
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\[
{} x^{\prime \prime }-5 x^{\prime }+6 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+5 x = 0
\]
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\[
{} x^{\prime \prime }+3 x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 0
\]
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\[
{} x^{\prime \prime }+x = 0
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 0
\]
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\[
{} x^{\prime \prime }-x = t^{2}
\]
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\[
{} x^{\prime \prime }-x = {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right )
\]
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\[
{} x^{\prime \prime }-x^{\prime }+x = \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right )
\]
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\[
{} x^{\prime \prime }+x = \cos \left (t \right )
\]
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\[
{} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y = 0
\]
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\[
{} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right ) = 0
\]
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\[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\]
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\[
{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\]
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\[
{} \theta ^{\prime \prime } = -p^{2} \theta
\]
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\[
{} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}
\]
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\[
{} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}
\]
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\[
{} \theta ^{\prime \prime }-p^{2} \theta = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+12 y = 7 y^{\prime }
\]
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\[
{} r^{\prime \prime }-a^{2} r = 0
\]
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\[
{} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y = \sin \left (x \right )+\frac {\sin \left (3 x \right )}{3}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )
\]
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\[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y^{\prime \prime } = -m^{2} y
\]
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\[
{} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime } = x y
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\]
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\[
{} y^{\prime \prime }-2 y y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{3} y = 0
\]
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\[
{} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
\]
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\[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 0
\]
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\[
{} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+2 y = x
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x
\]
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\[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
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\[
{} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\]
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\[
{} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\]
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\[
{} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\]
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\[
{} e y^{\prime \prime } = -P \left (L -x \right )
\]
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\[
{} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\]
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\[
{} e y^{\prime \prime } = P \left (-y+a \right )
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime } = 2 x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x
\]
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\[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \csc \left (x \right )^{2} = \cos \left (x \right )
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\]
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