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ODE |
Mathematica |
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
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\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\]
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\[
{} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }-2 y^{\prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = \ln \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1
\]
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\[
{} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime } = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = x
\]
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\[
{} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = x
\]
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\[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 4 x
\]
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\[
{} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2}
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = x^{2}+\frac {1}{x^{2}}
\]
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\[
{} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = x^{2} \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = x \ln \left (x \right )
\]
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\[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2}
\]
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\[
{} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right )
\]
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\[
{} x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4
\]
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\[
{} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x
\]
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\[
{} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
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\[
{} \left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\]
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\[
{} y^{\prime \prime } \sin \left (x \right )-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y = 2
\]
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\[
{} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\]
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\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
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\[
{} y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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\[
{} \cos \left (x \right )^{2} y^{\prime \prime } = 1
\]
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\[
{} x^{3} y^{\prime \prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime } \csc \left (x \right )^{2} = 1
\]
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\[
{} y^{\prime \prime } \sqrt {a^{2}+x^{2}} = x
\]
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\[
{} x^{2} y^{\prime \prime } = \ln \left (x \right )
\]
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\[
{} y^{3} y^{\prime \prime } = a
\]
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\[
{} y^{\prime \prime }+\frac {a^{2}}{y} = 0
\]
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\[
{} y^{\prime \prime } = y^{3}-y
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{2 y}
\]
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\[
{} y^{\prime \prime } = x y^{\prime }
\]
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\[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\]
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\[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = a x
\]
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\[
{} x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0
\]
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\[
{} x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = x
\]
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\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime } = a {y^{\prime }}^{2}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\]
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\[
{} a^{2} y^{\prime \prime } y^{\prime } = x
\]
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\[
{} y^{\prime \prime \prime } y^{\prime \prime } = 2
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} y^{\prime } = x y^{\prime \prime }+\sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime \prime } = \lambda y^{\prime \prime }
\]
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\[
{} n \,x^{3} y^{\prime \prime \prime } = y-x y^{\prime }
\]
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\[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2} = 3 y y^{\prime }
\]
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\[
{} 2 x^{2} y y^{\prime \prime }+y^{2} = x^{2} {y^{\prime }}^{2}
\]
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\[
{} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}}
\]
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