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Mathematica |
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\[
{} 2 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right .
\]
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\[
{} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right .
\]
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\[
{} y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right .
\]
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\[
{} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x
\]
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\[
{} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0
\]
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\[
{} x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\]
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\[
{} x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime }+4 y^{\prime } x^{2}+3 y = 0
\]
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\[
{} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0
\]
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\[
{} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+\lambda y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-5 y^{\prime }+x y = 0
\]
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\[
{} x y^{\prime }-3 y = k
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-5 y^{\prime }+x y = 0
\]
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\[
{} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0
\]
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\[
{} 16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime }+\sin \left (x +y\right )^{2} = 0
\]
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\[
{} x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x
\]
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\[
{} x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\]
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\[
{} y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}}
\]
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\[
{} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x y^{\prime } = x +\frac {y}{2}
\]
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\[
{} 2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {2 y-x +5}{2 x -y-4}
\]
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\[
{} y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7}
\]
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\[
{} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}}
\]
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\[
{} y^{\prime } = \frac {x -2 y+5}{y-2 x -4}
\]
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\[
{} y^{\prime } = \frac {3 x -y+1}{2 x +y+4}
\]
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\[
{} 2 y^{\prime }+x = 4 \sqrt {y}
\]
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\[
{} 2 x y^{\prime }+y = y^{2} \sqrt {x -x^{2} y^{2}}
\]
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\[
{} \frac {2 x y y^{\prime }}{3} = \sqrt {x^{6}-y^{4}}+y^{2}
\]
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\[
{} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0
\]
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\[
{} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 y^{\prime } x^{2}+8 x^{3} y = 0
\]
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\[
{} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 2 \,{\mathrm e}^{x} x -1
\]
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\[
{} x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
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\[
{} x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right )
\]
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\[
{} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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\[
{} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = x^{2}-1
\]
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\[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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\[
{} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right )
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\]
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\[
{} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x}
\]
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\[
{} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\]
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\[
{} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = -\frac {y}{t}-1-y^{2}
\]
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\[
{} y y^{\prime }+x = a {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } x^{2}+\left (x^{4}+2 x -1\right ) y = 0
\]
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\[
{} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right )
\]
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\[
{} \sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0
\]
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\[
{} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0
\]
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\[
{} x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2}
\]
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\[
{} x x^{\prime \prime }-{x^{\prime }}^{2} = 0
\]
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\[
{} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0
\]
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\[
{} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}} = 0
\]
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\[
{} \left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1
\]
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\[
{} a y^{\prime \prime } y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}}
\]
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\[
{} x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\]
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\[
{} \left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0
\]
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\[
{} \left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (1+x \right ) \eta ^{\prime }+\left (k +1\right ) \eta = 0
\]
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\[
{} x y^{\prime }-y = x \sqrt {-y^{2}+x^{2}}\, y^{\prime }
\]
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\[
{} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0
\]
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\[
{} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime \prime }-x y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0
\]
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\[
{} y^{\prime } = \frac {x^{2}+x}{y-y^{2}}
\]
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