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ODE |
Mathematica |
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Sympy |
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\[
{} y^{\prime \prime }+y-a \cos \left (b x \right ) = 0
\]
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\[
{} y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right ) = 0
\]
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\[
{} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0
\]
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\[
{} y^{\prime \prime }+a^{2} y-\cot \left (a x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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\[
{} x^{\prime \prime } = -3 \sqrt {t}
\]
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\[
{} x^{\prime \prime }+x^{\prime } = 3 t
\]
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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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\[
{} x^{\prime \prime }+x = \tan \left (t \right )
\]
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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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\[
{} x^{\prime \prime }+x = \frac {1}{t +1}
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\]
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\[
{} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\]
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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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\[
{} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2}
\]
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\[
{} y^{\prime \prime }+y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}
\]
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