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ODE |
Mathematica |
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Sympy |
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\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+2 x = 0
\]
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\[
{} t^{2} x^{\prime \prime }-6 x = 0
\]
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\[
{} 2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\]
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\[
{} x^{\prime \prime } = -3 \sqrt {t}
\]
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\[
{} x^{\prime }+t x^{\prime \prime } = 1
\]
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\[
{} \frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\]
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\[
{} x^{\prime \prime }+x^{\prime } = 3 t
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime } = 0
\]
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\[
{} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime } = 0
\]
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\[
{} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+4 x = 0
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+6 x = 0
\]
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\[
{} x^{\prime \prime }+9 x = 0
\]
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\[
{} x^{\prime \prime }-12 x = 0
\]
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\[
{} 2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\]
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\[
{} \frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 12
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\]
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\[
{} x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\]
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\[
{} x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\]
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\[
{} x^{\prime \prime }+x = t^{2}
\]
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\[
{} x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\]
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\[
{} x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }-4 x = \cos \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }-2 x^{\prime } = 4
\]
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\[
{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\]
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\[
{} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\]
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\[
{} x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\]
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\[
{} x^{\prime \prime } = -\frac {x}{t^{2}}
\]
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\[
{} x^{\prime \prime } = \frac {4 x}{t^{2}}
\]
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\[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\]
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\[
{} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\]
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\[
{} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0
\]
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\[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0
\]
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\[
{} t^{2} x^{\prime \prime }+t x^{\prime } = 0
\]
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\[
{} t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\]
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\[
{} x^{\prime \prime }+t^{2} x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }+x = \tan \left (t \right )
\]
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\[
{} x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }-x = \frac {1}{t}
\]
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\[
{} t^{2} x^{\prime \prime }-2 x = t^{3}
\]
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\[
{} x^{\prime \prime }+x = \frac {1}{t +1}
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\]
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\[
{} x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\]
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\[
{} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\]
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\[
{} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\]
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\[
{} x^{\prime \prime }+t x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }-t x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0
\]
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\[
{} x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0
\]
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\[
{} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0
\]
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\[
{} x^{\prime \prime }-x^{\prime }-6 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 0
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }-x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\]
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\[
{} x^{\prime \prime }+9 x = \sin \left (3 t \right )
\]
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\[
{} x^{\prime \prime }-2 x = 1
\]
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\[
{} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\]
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\[
{} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right )
\]
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\[
{} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\]
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\[
{} x^{\prime \prime }-x = \delta \left (t -5\right )
\]
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\[
{} x^{\prime \prime }+x = \delta \left (t -2\right )
\]
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\[
{} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\]
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\[
{} x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\]
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\[
{} x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = 0
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-12 y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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