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ODE |
Mathematica |
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\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
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\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )
\] |
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\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}
\] |
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\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
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\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
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\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime } = 2 y
\] |
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\[
{}x y^{\prime }+y = x^{2}
\] |
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\[
{}y^{\prime }+2 x y = x
\] |
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\[
{}2 y^{\prime }+x \left (y^{2}-1\right ) = 0
\] |
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\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = -x
\] |
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\[
{}y^{\prime } = -x \sin \left (x \right )
\] |
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\[
{}y^{\prime } = x \ln \left (x \right )
\] |
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\[
{}y^{\prime } = -x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime } = \sin \left (x^{2}\right ) x
\] |
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\[
{}y^{\prime } = \tan \left (x \right )
\] |
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\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
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\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
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\[
{}y^{\prime } = x \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = -\frac {y \left (1+y\right )}{x}
\] |
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\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
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\[
{}y^{\prime } = {| y|}+1
\] |
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\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
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\[
{}y^{\prime }+a y = 0
\] |
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\[
{}y^{\prime }+3 x^{2} y = 0
\] |
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\[
{}x y^{\prime }+y \ln \left (x \right ) = 0
\] |
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\[
{}x y^{\prime }+3 y = 0
\] |
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\[
{}x^{2} y^{\prime }+y = 0
\] |
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\[
{}y^{\prime }+\frac {\left (1+x \right ) y}{x} = 0
\] |
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\[
{}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
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\[
{}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0
\] |
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\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0
\] |
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\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
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\[
{}y^{\prime }+\tan \left (k x \right ) y = 0
\] |
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\[
{}y^{\prime }+3 y = 1
\] |
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\[
{}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x}
\] |
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\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
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\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}
\] |
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\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
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\[
{}y^{\prime }+\frac {4 y}{x -1} = \frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}}
\] |
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\[
{}x y^{\prime }+\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
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\[
{}2 y+x y^{\prime } = \frac {2}{x^{2}}+1
\] |
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\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )
\] |
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\[
{}\left (1+x \right ) y^{\prime }+2 y = \frac {\sin \left (x \right )}{1+x}
\] |
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\[
{}\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y = \left (x -2\right )^{3}
\] |
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\[
{}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}}
\] |
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\[
{}x^{2} y^{\prime }+3 x y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime }+7 y = {\mathrm e}^{3 x}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+4 x y = \frac {2}{x^{2}+1}
\] |
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\[
{}x y^{\prime }+3 y = \frac {2}{x \left (x^{2}+1\right )}
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
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\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
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\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}}
\] |
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\[
{}2 y+x y^{\prime } = 8 x^{2}
\] |
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\[
{}x y^{\prime }-2 y = -x^{2}
\] |
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\[
{}y^{\prime }+2 x y = x
\] |
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\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}}
\] |
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\[
{}\left (x +2\right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (x +2\right )^{3}}
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right )
\] |
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\[
{}x y^{\prime }-2 y = -1
\] |
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\[
{}\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right ) = -1
\] |
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\[
{}{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right ) = \frac {1}{x^{2}}
\] |
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\[
{}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2}
\] |
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\[
{}\frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )} = -\frac {3}{x^{2}}
\] |
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\[
{}y^{\prime } = \frac {3 x^{2}+2 x +1}{y-2}
\] |
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\[
{}\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }+y^{2}+y = 0
\] |
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\[
{}\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0
\] |
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\[
{}x^{2} y y^{\prime } = \left (y^{2}-1\right )^{{3}/{2}}
\] |
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\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime } = \left (x -1\right ) \left (y-1\right ) \left (y-2\right )
\] |
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\[
{}\left (y-1\right )^{2} y^{\prime } = 2 x +3
\] |
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\[
{}y^{\prime } = \frac {x^{2}+3 x +2}{y-2}
\] |
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\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
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\[
{}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime }+\frac {\left (1+y\right ) \left (y-1\right ) \left (y-2\right )}{1+x} = 0
\] |
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\[
{}y^{\prime }+2 x \left (1+y\right ) = 0
\] |
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\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right )
\] |
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\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
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\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
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\[
{}y^{\prime } = 2 y-y^{2}
\] |
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\[
{}x +y y^{\prime } = 0
\] |
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\[
{}y^{\prime }+x^{2} \left (1+y\right ) \left (y-2\right )^{2} = 0
\] |
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\[
{}\left (1+x \right ) \left (x -2\right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
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