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# |
ODE |
CAS classification |
Solved? |
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\[
{}y^{\prime } = x +\frac {y^{2}}{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = t +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = t^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = t +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = t^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = a \,x^{2}+b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}x y^{\prime }+a +x y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}y^{2}+y^{\prime } = \frac {a^{2}}{x^{4}}
\] |
[_rational, _Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}c y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }+y^{2}+a \,x^{m} = 0
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }+y^{2} a -b \,x^{\nu } = 0
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}x y^{\prime }+a +x y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2} a \right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{4} \left (y^{2}+y^{\prime }\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2} a +b \,x^{n}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x^{2} a y^{2}+b
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}x^{\prime } = t^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}x^{\prime } = t -x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = t -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4 t
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }-y^{2} = x
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }+t^{2} = y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+\frac {1}{x^{4}}
\] |
[_rational, [_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
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